


















AND 


NAVIGATION, 

WITH DESCRIPTIONS OF THE INSTRUMENTS AND THE 

NECESSARY TABLES. 


BY CHABLES DAVIES, LL. D., 


\ » 


AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN, 
ELEMENTS OF DESCRIPTIVE GEOMETRY, SHADES, SHADOWS, AND PER¬ 
SPECTIVE, ANALYTICAL GEOMETRY, DIFFERENTIAL AND 
INTEGRAL CALCULUS. 


REVISED EDITION. 


o 

y $ .) 

1 > 


NEW YORK: 

A. S. BARNES & BURR, 51 & 53 JOHN STREET. 

SOLD BY BOOKSELLERS, GENERALLY, THROUGHOUT THE UNITED STATES. 

1800. 






Babies’ 


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•O' 



must jtrf 


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Babies’ primary giritbmetic and STable^SSooft—Designed for Beginners; 
containing the elementary tables of Addition, Subtraction, Multiplication, 
Division, and Denominate Numbers ; with a large number of easy and prac¬ 
tical questions, both mental and written. 


Babies’J^irst Wessons in Arithmetic—Combining the Oral Method with the 
Method of Teaching the Combinations of Figures by Sight. 

Babies’ Jmtcllcctual Arithmetic—An Analysis of the Science of Numbers, with 
especial reference to Mental Training and Development. 

Babies’ Neb) School Arithmetic—Analytical and Practical. 

Stci) to Babies* "Neb) School Arithmetic. 

Babies’ CKrammar of Arithmetic—An Analysis of the Language of Numbers 
and the Science of Figures. 

Babies’ T^cb) FTmbeottr Arithmetic—Embracing the Science of Numbers, and 
their Applications according to the most Improved Methods of Analysis and 
Cancellation. 


Bci) to Babies* Neb) timber situ Arithmetic. 

Babies’ Hlcmentari) Algebra—Embracing the First Principles of the Science, 

Sites to Babies’ Blemcntayw Algebra. 

Babies’ Blementary CSrometr^ and ©rtgonomctrp—With Applications in 
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Babies’ practical Mathematics—With Drawing and Mensuration applied to 
the Mechanic Arts. 

Babies* SSnibersits? Algebra—Embracing a Logical Development of the 
Science, with graded examples. 

Babies* ISourbon’s Algebra—Including Sturm’s and Horner’s Theorems, 
and practical examples. 

Babies’ 3Lcgcnbre’s ©Jconretrij anb ^Trigonometry—Revised and adapted to 

the course of .Mathematical Instruction in the United States. 

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Babies’ Elements of Sueberjing and Nabigation—Containing descriptions 
of the Instruments and necessary Tables. 

Babies* Analytical (Geometry—Embracing the Equations of the Point, the 
Straight Line, the Conic Sections, and Surfaces of the first and second order. 

Babies* Biffereutial and integral ©alculus. 

Babies’ Bcscriptibc ©fcometry—Withits application to Spherical Trigonome¬ 
try, Spherical Projections, and Wafp^d ^Surfaces. 

Babies’ i&habes, iSpa^ohs, and 3j3e?»peVttbe. 

Babies’ 2Logtc anb (Utility of Mathematics—With the best methods of In¬ 
struction Explained and Illustrated. 

Babies’ anti Merit’s Mathematical -Dictionary anb ©ndopebia of Mathe* 
mat'cal Science—Comprising Definitions of all thef terms employed in 
Mathematics—an Analysis of each Branch, and of the whole, as forming a 
single Science. 


Entered according to Act of Congress, in the vear one thousand eight hundred and fiftv- 
one, by Charles Davies, in the Clerk’s Office of the District Court of the Uuited States 
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-70/0 

PREFACE. 


The Elements of Surveying, first published in 1880, 
was designed as a text-book for the pupils of the Military 
Academy, and in its preparation little regard was had to 
the supposed wants of other institutions. 

The work, however, was received by the public with 
more favor than was anticipated, and soon became a lead¬ 
ing text-book in the Colleges, the Academies, and the 
higher grade of Schools. 

For the purpose of adapting it, more fully, to the sup¬ 
posed wants of these institutions many changes have been 
made, since its first publication, and the present edition 
will be found to differ, in many respects, from those which 
have preceded. 

It has been the intention to begin with the very ele¬ 
ments of the subject, and to combine those elements in 
the simplest manner, so as to render the higher branches 
of plane surveying comparatively easy. All the instru¬ 
ments needed for plotting have been carefully described; 
and the uses of those required for the measurement of 
angles are fully explained. 

The conventional signs adopted by the Topographical 
Bureau, which are now used by the United States Engi¬ 
neers in all their Charts and Maps, are given in plate® 
5 and 6. 

Should these signs be generally adopted in the country, 
if would give entire uniformity to all maps and delinea¬ 
tions of the ground, and would establish a kind of lan¬ 
guage by which all the peculiarities o° soil and surface 
could be accurately represented. 




1Y 


PREFACE. 


A section has also been added on Geodesy. This 
branch of Surveying is extensively applied in the Coast 
Survey, and now forms an important element of a practi* 
cal or scientific education. 

A full account is also given of the manner of survey- 
ing the public lands; and, although the method is simple, 
it has, nevertheless, been productive of great results, by 
defining, with mathematical precision, the boundaries of 
lands in the new States, and thus settling their titles on 
an indisputable basis. 

This method was originated by Col. Jared Mansfield, 
whose great acquirements in science introduced him to the 
notice of President Jefferson, by whom he was appointed 
surveyor-general of the North-Western Territory 0 

May it be permitted to one of his pupils, and a gradu¬ 
ate of the Military Academy, further to add, that at the 
organization of the institution in 1812, he was appointed 
Professor of Natural and Experimental Philosophy. This 
situation he filled for sixteen years, when he withdrew 
from the Academy to spend the evening of his life in re¬ 
tirement and study. His pupils, who had listened to his 
instructions with delight, who honored his learning and 
wisdom, and had been brought near to him by his kind 
and simple manners, have placed his portrait in the public 
library, that the institution might possess an enduring 
memorial of one of its brightest ornaments and distin¬ 
guished benefactors. 

At the solicitation of several distinguished teachers, there 
is added, in the present edition, an article on Plane Sail¬ 
ing, most of which has been taken, by permission of the 
author, from an excellent work on Trigonometry and its 
applications, by Professor Charles W. Hackley. 

Fishkill Landing, 

July, 1851. 


C O N T E N T S . 


BOOK I. 

SECTION I. 

PAGE. 

Of Logarithms,.>.. 9 

Table of Logarithms,. 11 

Multiplication by Logarithms,. 15 

Division by Logarithms,. 16 

Arithmetical Complement,. 17 

SECTION II. 

Geometrical Definitions,. 19 

Geometrical Constructions,. 25 

Description of Instruments,. 25 

Dividers,. 25 

Ruler and Triangle,. 25 

Scale of Equal Parts,......-.. 27 

Diagonal Scale of Equal Parts,.,. 27 

Scale of Chords,. 29 

Semicircular Protractor,_ 30 

Sectoral Scale of Equal Parts,. 30 

Gunter’s Scale,. 32 

Solution of Problems,. 32 

SECTION III. 

Plane Trigonometry,. 38 

Division of the Circumference,. 38 

Definitions of the Trigonometrical Lines,. 39 

Table of Natural Sines,... 40 

Table of Logarithmic Sines,. 41 

Theorems,. 44 

Solutior of Triangles,. 48 

Solution of Right-Angled Triangles,. 54 

Application to Heights and Distances,. 55 





























VI 


CONTENTS. 


BOOK II. 

4 

PLANE SURVEYING. 

SECTION I. 

PAO . 

Definitions,. h« 

Measurement of Lines and Angles,. fin 

Measures for Distances,. 6fi 

To Measure a Horizontal Line,. . . 67 

Measurement of Angles,. 69 

Of the Theodolite,. 69 

Verniers,. 75 

To Measure a Horizontal Angle with the Theodolite,. 77 

To Measure a Vertical Angle,. 78 

Measurements with the Tape or Chain,.. 79 

Surveying Cross,. 81 

SECTION II. 

Area, or Contents of Ground,.”. 85 

Of Laying out Land,. 96 

SECTION III. 

The Circumferenter, or Surveyor’s Compass,. 98 

Surveying with the Compass, Definitions, etc.,. 99 

Field Operations,. 102 

Traverse Table,. 105 

Of Balancing the Work,. 109 

Of the Double Meridian Distances of the Courses,. 112 

Of Finding the Area,._•. 114 

First Method of Plotting,. 117 

Second Method of Plotting,. 117 

Problems,. 118 

Offsets,. 122 

Of Supplying Omissions in the Field Notes,. 124 

To Determine the .\ngle between two Courses,. 126 

Of Dividing Land,. 127 

SECTION IV. 

Method of Surveying the Public Lands,. 131 

Variation of the Needle,. 134 

Method of Ascertaining the Variations,. 138 

To Find the True Meridian with the Theodolite,. 140 

To Find the True Meridian with the Compass,. 141 


































CONTENTS. 


Vll 


BOOK III. 

LEVELLING AND TOPOGRAPHICAL SURVEYING. 

SECTION I. 

PAGE. 

Of Levelling,. 145 

The Y Level,. 147 

The Water Level,. 150 

Levelling Staves,. 151 

Levelling in the Field,. 153 

Difference of Level between Two Points,. 153 

Example,. 154 

Levelling for Section,. 157 

Plotting the Section or Profile,. 158 

SECTION 11. 

Topographical Surveying,. 159 

Field Notes,. 166 

P l otting the Work,. 167 

BOOK IY. 

GEODESIC, TRIGONOMETRIC, AND MARITIME 

SURVEYING. 

SECTION I. 

Geodesic and Trigonometric Surveying,. 172 

Preliminary Reconnoissance and Establishment of Signals,. 174 

Measurement of a Base Line,. 176 

Triangulation,. 178 

Filling up the Survey,. 181 

Use of the Compass,. 1 S 1 

The Plane Table—Its Uses,. 183 

To Measure a Horizontal Angle,. 185 

To Determine Lines in Extent and Position,. 185 

Of Changing the Paper,. 187 

Reduction to the Centre,. 189 

Spherical Excess,. 190 

Plotting the Triangulation,. 192 

The Circular Protractor,. 192 

To Lay off an Angle with the Protractor,. 193 

First Method of Plotting,. 193 

Second Method of Plotting,. 194 

Method of Chords,. 195 

To Lay off an Angle,. 196 

SECTION 1. 

Maritime Surveying,. 197 


































Vlll 


CONTENTS. 


BOOK Y. 

OF NAVIGATION. 

SECTION I. 

PAGE. 

Definitions,... 201 

SECTION II. 

Of Plane Sailing,.205 

SECTION III. 

Of Traverse Sailing,.207 

Of Plotting,.209 

SECTION IV. 

Parallel Sailing,. 211 

SECTION V. 

Middle Latitude Sailing,.214 

Mercator’s Sailing,.218 

Mercator’s Chart,.1... 221 

Line of Meridional Parts on Gunter’s Scale,. 222 











ELEMENTS 0E SUEYEYING. 


BOOK I. 

SECTION I. 

OF LOGARITHMS. 

1. The logarithm of a number is the exponent of the power 
to which it is necessary to raise a fixed number , in order to 
produce the first number . 

This fixed number is called the base of the system, and 
may be any number except 1: in the common system. 10 
is assumed as the base. 

2. If we form those powers of 10, which are denoted 
by entire exponents, we shall have 

10 °= 1 10 1 = 10 , 10 3 = 1000 

10* = 100, 10 4 = 10000, &c., &c., 

From the above table, it is plain, that 0, 1, 2, 3, 4, &c., 
are respectively the logarithms of 1, 10, 100, 1000, 10000, 
&c.; we also see, that the logarithm of any number be¬ 
tween 1 and 10, is greater than 0 and less than 1: thus, 

log 2 = 0.301030. 

The logarithm of any number greater than 10, and less 
than 100, is greater than 1 and less than 2: thus, 

log 50 = 1.698970. 

The logarithm of any number greater than 100, and 
less than 1000, is greater than 2 and less than 3: thus, 

log 126 - 2.100371, &c. 



10 


ELEMENTS OF SURVEYING 


[BOOK I 


If the above principles be extended to other numbers, 
it will appear, that the logarithm of any number, not an 
exact power of ten, is made up of two parts, an entire and 
a decimal part. The entire part is called the characteristic 
of the logarithm , and is always one less than the number of 
places of figures in the given number. 

3. The principal use of logarithms, is to abridge nm 
merical computations. 

Let M denote any number, and let its logarithm bs 
denoted by m; also let N denote a second number whose 
logarithm is n; then, from the definition, we shall have, 

10 ,n = M (1) 10 n - N (2). 

Multiplying equations (1) and (2), member by member 
we have, 

10 m + n _ jy ^ jy or ^ m n —\ 0 g (q/ x TV") • hence, 

The sum of the logarithms of any two numbers is equal t 
the logarithm of their product. 

4. Dividing equation (1) by equation (2), member by 
member, we have, 

m-n M If 

10 = -y or, m — n = log : hence, 

The logarithm of the quotient of two numbers, is equal to 
the logarithm of the dividend diminished by the logarithm of 
the divisor. 

% 

5. Since the logarithm of 10 is 1, the logarithm of the 
pn'oduct of any number by 10, will be greater by 1 than the 
logarithm of that number; also, the logarithm of the quotient 
of any number divided by 10, will be loss by 1 than the 
logarithm of that number. 

Similarly, it may be shown that if any number be mul- 
iplied by one hundred, the logarithm of the product will 
be greater by 2 than the logarithm of that number; and 
if airp number be divided by one hundred, the logarithm 
of the quotient will be less by 2 than the logarithm of 
that number, and so on. 


SEC. I] 


LOGARITHMS. 


11 


EXAMPLES. 


log 327 is 2.514548 

log 32,7 “ 1.514548 

log 3.27 “ 0.514548 

log .327 “ 1.514548 

log .0327 “ 2.514548 


From the above examples, we see, that in a numbei 
composed of an entire and decimal part, we may change 
the place of the decimal point without changing the deci 
mal part of the logarithm; but the characteristic is dimin¬ 
ished by 1 for every place that the decimal point is removed tc 
the left. 

In the logarithm of a decimal, the characteristic becomes 
negative, and is numerically 1 greater than the number of 
ciphers immediately after the decimal point. The negative 
sign extends only to the characteristic, and is written over 
it, as in the examples given above. 

TABLE OF LOGARITHMS. 

6. A table of logarithms, is a table in which are writ¬ 
ten the logarithms of all numbers between 1 and some 
given number. The logarithms of all numbers between 1 
and 10,000 are given in the annexed table. Since rules 
have been given for determining the characteristics of 
logarithms by simple inspection, it has not been deemed 
necessary to write them in the table, the decimal part 
only being given. The characteristic, however, is given 
for all numbers less than 100. 

The left hand column of each page of the table, is the 
column of numbers, and is designated by the letter FT; 
the logarithms of these numbers are placed opposite them 
on the same horizontal line. The last column on each 
page, headed D, shows the difference between the loga¬ 
rithms of two consecutive numbers. This difference is 
found by subtracting the logarithm under the column 
headed 4, from the one in the column headed 5 in the 
same horizontal line, and is nearly a mean of the differ¬ 
ences of any two consecutive logarithms on this line. 


12 


ELEMENTS OF SURVEYING. 


[BOOK I 


To find , from the table , logarithm of any number. 

7. If the number is less than 100, look on the first page 
of the table, in the column of numbers under IST, until the 
number is found: the number opposite is the logarithm 
ought: Thus, 

log 9 = 0.954243. 


When the number is greater than 100 and less than 10000. 

8 . Find in the column of numbers, the first three figures 
of the given number. Then pass across the-page along a 
horizontal line until you come into the column under the 
fourth figure of the given number: at this place, there are 
four figures of the required logarithm, to which two figures 
taken from the column marked 0 , are to be prefixed. 

If the four figures already found stand opposite a row 
of six figures in the column marked 0 , the two left hand 
figures of the six, are the two to be prefixed; but if they 
stand opposite a row of only four figures, you ascend the 
column till you find a row of six figures; the two left 
hand figures of this row are the two to be prefixed. If 
you prefix to the decimal part thus found, the characteristic, 
70 u will have the logarithm sought: Thus, 

log 8979 = 3.953228 

log .08979 = 2.953228 

% 

If, however, in passing back from the four figures found 
to the 0 column, any clots be met with, the two figures 
to be prefixed must be taken from the horizontal line di¬ 
rectly below: Thus, 

log 3098 = 3.491081 
log 30.98 = 1.491081 

If the logarithm falls at a place where the dots occur 
0 must be written for each dot, and the two figures to hi 
prefixed are, as before, taken from the line belo>v: Thus, 

log 2188 = 3.340047 
log .2188 = 1.340047 


* 


SEC. L] 


LOGARITHMS. 


.13 


When the number exceeds 10,000. 

9. The characteristic is determined by the rules already 
given. To find the decimal part of the logarithm: place 
a decimal point after the fourth figure from the left 
hand, converting the given number into a whole numbei 
and decimal. Find the logarithm of the entire part by the 
rule just given, then take from the right hand column of 
the page, under D, the number on the same horizontal 
line with the logarithm, and multiply it by the decimal 
part; add the product thus obtained to the logarithm al¬ 
ready found, and the sum will be the logarithm sought. 

If, in multiplying the number taken from the column 
D, the decimal part of the product exceeds .5, let 1 be 
added to the entire part; if it is less than .5, the decimal 
part of the product is neglected. 

EXAMPLE. 

1. To find the logarithm of the number 672887. 

The characteristic is 5.; placing a decimal point after 
the fourth figure from the left, we have 6728.87. The 
decimal part of the log 6728 is .827886, and the corres¬ 
ponding number in the column F is 65; then 65X .87= 
56.55, and since the decimal part exceeds .5, we have 57 
to be added to .827886, which gives .827943. 

Hence, log 672887 = 5.827943 

Similarly, log .0672887 = 2.827943 

The last rule has been deduced under the supposition 
that the difference of the numbers is proportional to the 
difference of their logarithms, which is sufficiently exact 
within the narrow limits considered. 

In the above example, 65 is the difference between the 
logarithm of 672900 and the logarithm of 672800, that is, 
it is the difference between the logarithms of two numbers 
jvhich differ by 100. 

We have then the proportion 

100 : 87 : : 65 : 56.55, 

Lence, 56.55 is the number to be added to the logarithm 
before found. 


;4 ELEMENTS OF SURVEYING. [BOOK 1. 

To find from the table the number corresponding to a given 

logarithm. 

10 . Search in the columns of logarithms for the decimal 
part of the given logarithm: if it cannot be found in the 
table, take out the number corresponding to the next less 
logarithm and set it aside. Subtract this less logarithm 
from the given logarithm, and annex to the remainder as 
many zeros as may be necessary, and divide this result by 
the corresponding number taken froyi the column marked 
D, continuing the division as long as desirable: annex the 
quotient to the number set aside. Point off, from the left 
hand, as many integer figures as there are units in the 
characteristic of the given logarithm increased by 1 ; the 
result is the required number. 

If the characteristic is negative, the number will be 
entirely decimal, and the number of zeros to be placed at 
the left of the number found from the table, will be equal to 
the number of units in the characteristic diminished by 1 . 

This rule, like its converse, is founded on the supposi¬ 
tion that the difference of the logarithms is proportional 
to the difference of their numbers within narrow limits. 

EXAMPLE. 

1. Find the number corresponding to the logarithm 
8.233568. 

The decimal part of the given logarithm is .233568 

The next less logarithm of the table is .233504, 

and its corresponding number 1712. - 

Their difference is - - - 64 

Tabular difference • 253)6400000(25 

Hence, the number sought 1712.25. 

The number corresponding to the logarithm 3.23356S 
is .00171225. 

2 . What is the number corresponding to the logarithm 

2.785407? Ans. .06101084. 

3. What is the number corresponding to the logarithm 

1.846741? Am. .702653. 



SEC. I] 


LOGARITHMS. 


15 


MULTIPLICATION BY LOGARITHMS. 

11. When it is required to multiply numbers by means 
of their logarithms, we first find from the table the loga¬ 
rithms of the numbers to be multiplied; we next add 
these logarithms together, and their sum is the logarithm 
of the product of the numbers (Art. 3). 

The term sum is to be understood in its algebraic 
sense; therefore, if any of the logarithms have negative 
characteristics, the difference between their sum and that 
of the positive characteristics, is to be taken; the sign of 
the remainder is that of the greater sum. 

EXAMPLES. 

1. Multiply 23.14 by 5.062. 

log 23.14 = 1.364363 
log 5.062 = 0.704322 

Product, 117.1347 . . . 2.068685 

2. Multiply 3.902, 597.16, and 0.0314728 together. 

log 3.902 = 0.591287 
log 597.16 = 2.776091 
log 0.0314728 = 2.497936 

Product, 73.8354 .... 1.865814 

Here, the 2 cancels the + 2, and the 1 carried from 
tile decimal part is set down. 

3 . Multiply 8.586, 2.1046, 0.8872, and 0.0294 together. 

log 8.586 = 0.554610 
log 2.1046 = 0.823170 
log 0.8372 = 1.922829 
log 0.0294 = 2.468347 

Product, 0.1857615 . . 1.268956 

In this example the 2, carried from the decimal part, 
cancels 2, and there remains 1 to be set down. 










16 


ELEMENTS OF SURVEYING. 


[BOOK 1 


DIVISION OF NUMBERS BY LOGARITHMS. 

12 . When it is required to divide numbers by means 
of their logarithms, we have only to recollect, that the 
subtraction of logarithms corresponds to the division of 
their numbers (Art. 4). Hence, if we find the logarithm 
of the dividend, and from it subtract the logarithm of the 
divisor, the remainder will be the logarithm of the quotient. 

This additional caution may be added. The difference 
of the logarithms, as here used, means the algebraic differ¬ 
ence; so that, if the logarithm of the divisor have a nega¬ 
tive characteristic, its sign must be changed to positive, 
after diminishing it by the unit, if any, carried in the sub¬ 
traction from the decimal part of the logarithm. Or, if 
the characteristic of the logarithm of the dividend is nega¬ 
tive, it must be treated as a negative number. 

EXAMPLES. 

1. To divide 24163 by 4567. 

log 24163 = 4.383151 
log 4567 = 3.659631 

Quotient, 5.29078 . . 0.723520 


2 . To divide 0.06314 by .007241. 

log 0.06314 = 2.800305 
log 0.007241 = 3.859799 

Quotient, 8.7198 . . 0.940506 


Here, 1 carried from the decimal part to the 3, changes 
it to 2, which being taken from 2, leaves 0 for the cha¬ 
racteristic. 

3. To divide 37.149 by 523.76. 

log 37.149 = 1.569947 
log 523.76 = 2.719133 

Quotient, 0.0709274 . 2.850814 








8 E C. I.J 


LOGARITHMS. 


17 


4. To divide 0.7438 by 12.9476. 

log 0.7438 = 1.871456 
log 12.9476 = 1.112189 

Quotient, 0.057447 . . 2.759267 

Here, the 1 taken from 1 , gives 2 for a result, as set 
down. 


ARTTHMET1 0AL COMPLEMENT. 

13. The Arithmetical complement of a logarithm is the 
number which remains after subtracting the logarithm 

O O 

from 10 . 

Thus, 10 - 9.274687 = 0.725313. 

Hence, 0.725313 is the arithmetical complement 

of 9.274687. 

14. We will now show that, the difference between two 
logarithms is indy found , by adding to the first logarithm the 
arithmetical complement of the logarithm to be subtracted, and 
then diminishing the sum by 10 . 

Let a — the first logarithm, 

b = the logarithm to be subtracted, 
and c— 10 —b — the arithmetical complement of o. 

Now the difference between the two logarithms will be 
expressed by a — b. 

But, from the equation c — 10 — b, we have 

c — 10 = — b, 

hence, if we place for — b its value, we shall have 

a — b — a + c —10, 

which agrees with the enunciation. 

When we wish the arithmetical complement of a loga¬ 
rithm, we may write it directly from the table, by subtract¬ 
ing the left hand figure from 9, then proceeding to the right , 
subtract each figure from 9 till we reach the last significant 
figure , which must be taken from 10 : this will be die same 
as taking the logarithm from 10 . 


o 

Ud 



IS 


ELEMENTS OF SURVEYING. 


[BOOK 5 


EXAMPLES. 

1. From 3.274107 take 2.104729. 

By common method. By arith. comp. 

3.274107 3.274107 

2.104729 its ar. comp. 7.895271 

Diff. 1.169378 Sum 1.169378 after sub 

tracting 10. 

Hence, to perform division by means of the arithmetical 
complement, we have the following 


KULE. 

To the logarithm of the dividend add the arithmetical com¬ 
plement of the logarithm of the divisor: the sum , after sub¬ 
tracting 10, will be the logarithm of the quotient. 

EXAMPLES. 


1. Divide 327.5 by 22.07. 


log 327.5 . 

2.515211 

log 22.07 ar. comp. 

8.656198 

Quotient, 14.839 . . . 

1.171409 

2 . Divide 0.7488 by 12.9476. 


log 0.7488 .... 

1.871456 

log 12.9476 ar. comp. 

8.887811 

Quotient, 0.057447 . . . 

2.759267 

In this example, the sum of the characteristics 

from which, taking 10, the remaind 

or is 2. 

3. Divide 37.149 by 523.76. 


log 37.149 .... 

1.569947 

log 523.76 ar. comp. 

7.280867 

Quotient, 0.0709273 . . 

2.850814 












S E C. 11] 


19 


GEOMETRICAL DEFINITIONS. 


4. Divide 0.875 by 25. 

5. Divide 3.141(3 by .944. 


Arts. 0.035. 
.4ns. 3.8279. 
A ns. 8.4281. 


6 . Divide 275(3 by 327. 

« 

7. Divide 672859 by 0.09657. 


Ana. 6967580.64. 


SECTION n 



1. Extension lias three dimensions, length, breadth, 
and thickness. 

2. Geometry is the science which has for its object: 
1st. The measurement of extension; and 2dlv. To dis- 

cover, by means of such measurement, the properties and 
relations of geometrical figures. 

3. A Point is that, which has place, or position, but 
not magnitude. 

4. A Line is length, without breadth or thickness. 

5. A Straight Line is one which 

lies in the same direction between any --- 

two of its points. 



6. A Broken Line is one made up 
of straight lines, not lying in the same 
direction. 


7. A Curve Line is one which 



changes its direction at every point. ^ x 

The word line when used alone, will designate a straight 
line; and.the word curve , a curve line. 

8. A Surface is that which has length and breadth 
without thickness. 




20 


ELEMENTS OF SURVEYING. 


[BOOK I. 


9. A Plane is a surface, such, that if any two of its 
points be joined by a straight line, such line will be wholly 
in the surface. 

10. Every surface, which is not a plane surface, or com¬ 
posed of plane surfaces, is a curved surface. 

11. A Solid, or Body is that which has length, breadth, 

and thickness: it therefore combines the three dimensions 

\ 

of extension. 

12. An Angle is the portion of a plane included be¬ 
tween two straight lines which meet at a common point 
The two straight lines are called the sides of the angle, 
and the common point of intersection, the vertex. 

Thus, the part of the plane includ¬ 
ed between AB and A C is called an 
angle: AB and AC are its sides, and A 
its vertex. 

An angle is sometimes designated A ^- b 

simply by a letter placed at the vertex, 
as, the angle A ; but generally, by three letters, as, the 
angle BAG or CAB, —the letter at the vertex being always 
placed in the middle. 

13. When a straight line meets an¬ 
other straight line, so as to make the 
adjacent angles equal to each other, 
each angle is called a right angle ; and 

the first line is said to be perpendicu- __ 

lur to the second. 


14. An Acute Angle is an angle 
less than a right angle. 



15. An Obtuse Angle is an angle 
greater than a right angle. 








SEC. II.] 


GEOMETRICAL DEFINITIONS 


21 


16. Two straight lines are said to 

be parallel, when being situated m__ 

the same plane, they cannot meet, how 
for soever, either way, both of them 
be produced. 

17. A Plane Figure is a portion of a plane terminat¬ 
ed on all sides by lines, either straight or curved. 

i 

18. A Polygon, or rectilineal fig¬ 
ure , is a portion of a plane terminat¬ 
ed on all sides by straight lines. 

The sum of the bounding lines is 
called the perimeter of the polygon. 

19. The polygon of three sides, the simplest of all, is 
called a triangle; that of four sides, a quadrilateral; that 
of five, a pentagon ; that of six, a hexagon; that of seven, 
a heptagon; that of eight, an octagon; That of nine, an 
nonagon ; that of ten, a decagon; and that of twelve, a 
dodecagon. 

20. An Equilateral polygon is one which has all its 
sides equal; an equiangular polygon, is one which has all 
its angles equal. 

21. Two polygons are mutually equilateral , when they 
have their sides equal each to each, and placed in the 
same order: that is to say, when following their bounding 
lines in the same direction, the first side of the one is 
equal to the first side of the other, the second to the 
second, the third to the third, and so on. 

22. Two polygons are mutually equiangular , when every 
angle of the one is equal to a corresponding angle of the 

other, each to each. 

23. Triangles are divided into classes with reference 
both to their sides and angles. 

1. An equilateral triangle is one 
which has its three sides equal. 









22 


ELEMENTS OF SURVEYING. 


[BOOK r. 


2. An isosceles triangle is one which 
has only two of its sides equal. 



3. A scalene triangle is one which has 
its three sides unequal. 



4. An acute-angled triangle is one 
which has its three angles acute. 



5. A right-angled triangle is one which 
has a right angle. The side opposite the 
right angle is called the hypothenuse , and 
the other two sides, the base and perpen¬ 
dicular . 



6. An obtuse-angled triangle is one 


fyhich has an obtuse angle. 



24. There are three kinds of Quadrilaterals: 


1. The trapezium , which has none of 
its sides parallel. 



2. The trapezoid , which has only two 
of its sides parallel. 



3. The parallelogram , which tas its 
opposite sides parallel. 














SEC. II.J GEOMETRICAL DEFINITIONS. 


9 q 

Si o 


25. There are fou r kinds of Parallelograms: 


1. The rhomboid , which has no right 

angle. 



2. The rhombus , or lozenge , which is 
an equilateral rhomboid. 


n 


3. The rectangle , which is an equian¬ 
gular parallelogram, but not equilateral. 



4. The square , which is both equilat¬ 
eral and equiangular. 



A Diagonal of a figure is a line 

O 

which joins the vertices of two angles 
not adjacent. 



EXPLANATION OF SIGNS. 

* 

26. The sign = is the sign of equality; thus, the ex¬ 
pression A — B, signifies that A is equal to B. 

27. To signify that A is smaller than I>, the expression 
A < B is used. 

28. To signify that A is greater than B\ the expression 
A > B is used; the smaller quantity being always at the 
vertex of the angle. 

29. The sign f- is called plus; it indicates addition. 














24 


ELEMENTS OF SURVEYING. 


[BOOK I 


30. The sign — is called m in us; it indicates subtraction: 
Thus, A + represents the sum of the quantities A 

and B; A — B represents their difference, or what remains 
after B is taken from A ; and A — BA- 0, or A 4- G — B, 
signifies that A and G are to be added together, and that 
B is to be subtracted from their sum. 

31. The sign X indicates multiplication : thus A X B 
represents the product of A and B. 

The expression Ax ( B-\- 0 — B) represents the product 
of A b}^ the quantity B+ C — D. If A + D were to be 
multiplied by A — B + C\ the product would be indicated 
thus; 

{A -f- IJ) X (A — B T (7), 

whatever is enclosed within the curved lines, being consid¬ 
ered as a single quantity. The same thing may also bo 
indicated by a bar: thus, 

aTab+ Cx B>, 

denotes that the sum of A, B and (7, is to be multiplied 
by D. 

82. A figure placed before a line, or quantity, serves 
as a multiplier to that line or quantity; thus, 3 AB signi 
fics that the line AB is taken three times; \A signifies the 
half of the angle A. 

83. The square of the line AB is designated by AB '; 

its cube by AB 2 , What is meant by the square and cube 
of a line is fully explained in Geometry. 


34. The sign indicates a root to be extracted; thus, 

V2 means the square-root of 2; -yj A X B means the square 
root of the product of A and B 








SEC. II.] GEOMETRICAL CONSTRUCTIONS. 


D 


GEOMETRICAL CONSTRUCTIONS. 

85. Before explaining the method of constructing geo* 
metrical problems, we shall describe some of the simpler 
Instruments and their uses. 

DIVIDERS. 



8(3. The dividers is the most simple and useful of the 
instruments used for drawing. It consists of two legs ba 
be which mav be easily turned around a joint at h. 

One of the principal uses of this instrument is to lay 
off on a line, a distance equal to a given line. 

For example, to lay oft on Cl) a distance equal to AB. 

For this purpose, place the forefin¬ 
ger on the joint of the dividers, and A i- B 

set one foot at A: then extend, with 

the thumb and other fingers, the c — }? D 

other leg of the dividers, until its foot reaches the point 
B. Then raise the dividers, place one foot at C\ and 
mark with the other the distance CE: this will evidently 
be equal to AB. 

RULER AND TRIANGLE. 




37. A lduler of convenient size, is about twenty 
in length, two inches wide, and a fifth of an inch in 


incln ? 
thick* 











26 


ELEMENTS OF SURVEYING. [BOOK I. 

ness. It should be made of a hard material, perfectly 
straight and smooth. 

The liypothenuse of the right-angled triangle, which is 
used in connection with it, should be about ten inches in 
length, and it is most convenient to have one of the sides 
considerably longer than the other. We can solve, with 
the ruler and triangle, the two following problems. 


I. To draw through a given point a line luhich shall be paral- 

lei to a given line. 


38. Let C be the given point, and AB the given line. 

Place the liypothenuse of the tri- c 

an^le against the edge of the ruler, 
and then place the ruler and triangle 
oil the paper, so that one of the 
sides of the triangle shall coincide exactly with AB: the 
triangle being below the line. 

O O 


A 


B 


Then placing the thumb and fingers of the left hand 
firmly on the ruler, slide the triangle with the other hand 
along the ruler until the side which coincided with AB 


reaches the point 0. Leaving the thumb of the left hand 
on the ruler, extend the fingers upon the triangle and hold 
it firmly, and with the right hand, mark with a pen or 
pencil, a line through C: this line will be parallel to AB. 


il. To draw through a given point a line luhich shall be per¬ 
pendicular to a given line. 

39. Let AB be the given line, and D the given point. 

Place the liypothenuse of the tri¬ 
angle against the edge of the ruler, as 

before. Then place the ruler and __ 

triangle so that one of the sides of A 
the triangle shall coincide exactly with the line AB. 
Then slide the triangle along the ruler until the other 
side reaches the point D: draw through D a right line, 
and it will be perpendicular to AB. 







^ E C. II] GEOMETRICAL C O N S T R U C T IO N S. 


27 


SCALE OF EQUAL PARTS. 

a 

40. A scale of equal parts is formed by dividing a line 
of a given length into equal portions. 

If, for example, the line ab of a given length, say one 
inch, be divided into any number of equal parts, as 10, 
the scale thus formed, is called a scale of ten parts to the 
inch. The line ab, which is divided, is called the unit oj 
the scale. This unit is laid off several times on the left 
of the divided line, and the points marked 1, 2, 8, &c. 

The unit of scales of equal parts, is, in general, either 
an inch, or an exact part of an inch. If, for example, ab, 
the unit of the scale, were half an inch, the scale would 
be one of 10 parts to half an inch, or of 20 parts to the 
inch. 

If it were required to take from the scale a line equal 
to two inches and six-tenths, place one foot of the dividers 
at 2 on the left, and extend the other to .6, which marks 
the sixth of the small divisions: the dividers will then 
embrace the required distance. 

DIAGONAL SCALE OF EQUAL PARTS. 


I .1 .2 n .u.5 .a .7 .8 .V h 


— 


XTT 


l 


a 


d J 1 - r 

7 - i~l7 (T f- I ■' 1 F 



-- 

!• i- n i-i-ri r i 

• 

» 

OJ) 

i i i i i i i i i i 


■OS 

n 

1 1 191 l.i 4 

1 

- 

• 07 

II 

1 1 1 1 1 1 1 

1 


■0(5 

11 1 1 1 1 1 1 1 


• 

■05 

LI 1 Id 1 1 1 1 

r 

• 

.0i 

11 II If 1 I 1 1 

» 

.03 

f 1 

1 1 1 1 1 1 



■02 

1 1 1 1 1 1 1 1 1 



.0 i 

ALT 

1 1 1 1 II 



2 2 a .1 .2 .2.-1 .5 ,G .7.8 .!) b 

h <J 


41. This scale is thus constructed. Take ah for the 
unit of the scale, which may be one inch, } or y of an 
inch, in length. On ab describe the square abed. Divide 
the sides ab and clc each into ten equal parts. Draw af 
and the other nine parallels as in the figure. 

Produce ba to the left, and lay off Ilie unit of the 
scale any convenient number of times, and mark the points 



























28 


ELEMENTS OF SURVEYING. 


[BOOK I 


1, 2, 3, &c. Then, divide the line ad imo ten equal parts, 
and through the points of division draw parallels to ah, as 
in the figure. 

Now, the small divisions of the line ab are each one- 
tenth (.1) of ab; they are therefore .1 of ac/, or 1 of ag 
or gh. 

If we consider the triangle adf we see that the base df 
is one-tenth of ad ) the unit of the scale. Since the distance 
from a to the first horizontal line above ab, is one-tenth of 
the distance ad, it follows that the distance measured on that 
line between ad and af is one-tenth of df: but since one-tenth 
of a 'tenth is a hundredth, it follows that this distance is 

' /-K 

one hundredth (.01) of the unit oMthe scale. A like dis¬ 
tance measured on the second line'will be two hundredths 
(.02) of the unit of the scale; on the third, .03;. on the 
fourth, .Of, &c. 

If it were required to take, in the dividers, the unit of 
the scale, and any number of tenths, place one foot of the 
dividers at 1, and extend the other to that figure between 
a and b which designates the tenths. If two or more 
units are required, the dividers must be placed on a point 
of division farther to the left. 

When units, tenths, and hundredths, are required, place 
one foot of the dividers where the vertical line through 
the point which designates the units, intersects the line 
which designates the hundredths: then, extend the dividers 
to that line between ad and be which designates the tenths: 
the distance so determined will be the one required. 

For example, to take off the distance 2.3-4, we place 
one foot of the dividers at l, and extend the other to e 
and to take off’ the distance 2.58, we place one foot of the 
dividers at p and extend the other to q. 

Remark I. Tf a line is so long that the whole of it 
cannot be taken from the scale, it must be divided, and 
the parts of it taken from the scale in succession. 

Remark II. If a line be given upon the paper, its 
length can be found by taking it in the dividers and ap 
plying it to the scale. 


6 E C. I L] GEOMETRICAL CO N S T R IT C TT 0 N S 


29 


SCALE OF CHORDS. 



42. If, with any ra 
rant CD, and then divi 
is called a degree. 



as AC, we describe the quad* 
into 90 equal parts, each part 


Through C, and each point of division, let a chord be 
drawn, and let the lengths of these chords be accurately 
laid off on a scale: such a scale is called a scale of chords. 
In the figure, the chords are drawn for every ten de¬ 
grees. 

The scale of chords being once constructed, the radius 
of the circle from which the chords were obtained, is 
known; for, the chord marked GO is always equal to the 
radius of the circle. A scale of chords is generally laid 
down on the scales which belong to cases of mathematical 
instruments, and is marked ciio. 


To lay off, at a given point, of a line, with the scale of chords, 

an angle equal to a given angle. 

43. Let AB be the line, and A the given point. 

Take from the scale the chord of 60 
degrees, and with this radius and the 
point A as a centre, describe the arc 
BC. Then take from the scale the 
chord of the given angle, say 30 de¬ 
grees, and with this line as a radius, and B as a centre, 
describe an arc cutting BC in C. Through A and C 
draw the line AC, and BAG will be the required angle. 







80 


ELEMENTS OF SURVEYING. 


[BOQK I. 


SEMICIRCULAR PROTRACTOR. 
C 



It consists of a brass semicircle, ABO, divided to hdf 
degrees. The degrees are numbered from 0 to 180, both 
ways; that is, from A to B and from B to A. The di¬ 
visions, in the figure, are made only to degrees. There 
is a small notch at the middle of the diameter AB, which 
indicates the centre of the protractor. 

To lay off an angle with a Protractor. 

45. Place the diameter AB on the line, so that the 
centre shall fall on the angular point. Then count the 
degrees contained in the given angle from A towards B, or 
from B towards A, and mark the extremity of the arc with 
a pin. Remove the protractor, and draw a line through 
the point so marked and the angular point: this line will 
make with the given line the required angle. 


SECTORAL SCALE OF EQUAL PARTS. 





















SEC. IT.] GEOMETRICAL CONSTRUCTION'S. 


81 


46. The sector is an instrument generally made of ivory 
or brass. It consists of two arms, or sides, which open 
by turning round a joint at their common extremity. 

There are several scales laid down on the sector: those, 
however, which are chiefly used in drawing lines and 
angles, are, the scale of chords already described, and the 
scale of equal parts now to be explained. 

On each arm of the sector, there is a diagonal line 
that passes through the point about which the arms turn: 
these diagonal lines are divided into equal parts. 

On the sectors which belong to the cases of English 
instruments, the diagonal lines are designated by the letter 
X, and numbered from fkd. centre of the sector, 1, 2, 8, 4, 
5, 6, 7, 8, 9, 10, to the'wo extremities. On the sectors 
which belong to cases of French instruments, they are de¬ 
signated, “ Les parties egales,” and numbered 10, 20, 80, 
40, &c., to 200. On the English sectors there are 20 equal 
divisions between anv two of the lines numbered 1, 2, 3 

c/ 7 7/ 

&c., so that there are 200 equal parts on the scale. 

The advantage of the sectoral scale of equal parts, h 
this— 

• ; 

When it is proposed to draw a line upon paper, on 
such a scale that.any number of parts of the line, 40 for 
example, shall be represented by one inch on the paper, or 
by any part of an inch, take the inch, or part of the inch, 
from the seals of inches on the sector: then, placing one 
foot of the ‘dividers at 40 on one arm of the sector, open 
the sector until the other foot reaches to the corresponding 
number on the other arm: then lay the sector on the table 
without varying the angle. 

Now, if we regard the lines on the sector as the sides 
of a' triangle, of which the line 40, measured across, is the 
base, it is plain, that if any other line be likewise meas 
ured across the angle of the sector, the bases of the tri 
angles, so formed, will be proportional to their sides 
Therefore, if we extend the dividers iTom 50 to 50, this 
distance will repiesent a line of 50, to the given scale, 
and similarly for other lines. 


32 ELE5ir:r?ra OF SURVEYING. [BOOK 1. 

Let it now be required to lay down a line of sixty* 
seven feet, to a scale of twenty feet to the inch. 

Take one inch from the scale of inches: then place 
one foot of the dividers at the twentieth division, and 
open the sector until the dividers will just reach the twen¬ 
tieth division on the other arm: the sector is then set to 
the proper angle; after which the required distance to be 
laid down on the paper is found by extending the divi¬ 
ders from the sixty-seventh division on one arm, to the 
sixty-seventh division on the other. 


GUNTER’S SCALE. 

47. This is a scale of two feet in length, on the faces 
of which a variety of scales is marked. The face on 
which the divisions of inches are made, contains, however, 
all the scales necessary for laying down lines and angles. 
These are, the scale of equal parts, the diagonal scale of 
equal parts, and the scale of chords, all of which have 
been described. 


SOLUTION OF PROBLEMS REQUIRING THE USE OF THE IN¬ 
STRUMENTS THAT HAVE BEEN DESCRIBED. 

I. At a given point in a given straight line , *to erect a perpen¬ 
dicular to the line. 

48. Let A be the given point, and BO the given line. 
From A lay off any two distances, 

AB and AC, equal to each other. 

Then, from the points B and (7, as 
centres, with a radius greater than BA ) 
describe two arcs intersecting each B a d 
other in I): draw AJ), and it will be the perpendicular 
required. 

IT. From a given point without a straight line , to let fall a 

perpendicular on the line. 

49. Let A be the given point, and Bl) the given line. 





SEC. II] GEOMETRICAL CONSTRUCTIONS. 


83 


From the point i as a centre, 
with, a radius sufficiently great, 
describe an arc cutting the line 
BD in the two points B and D: 
then mark a point E , equally dis¬ 
tant from the points B and D, 
and draw AE: AE will be the perpendicular required. 



III. At a point, in a given line, to make an angle equal to a 

given angle. 

50. Let A be the given point, AE the given line, and 
TKL the given angle. 

From the vertex iij as a 
centre, with any radius, describe 
the arc IL , terminating in the 
two sides of the angle. From ^ 1 A 

the point 1 as a centre, with a distance AE "espial. to K1 , 
describe the arc ED; then take the chord L^f, with which, 
from the point E as a centre, describe an arc cutting the 
indefinite arc DE ' in D ; draw A D, and the angle EAD 
will be equal to the given angle E 




LV. To divide a given angle, or a given arc } into two equal 

parts. 

51. Let G be the given angle, and AEB the arc which, 
measures it. 

From the points A and B as 
centres, describe with the same 
radius two arcs cutting each other 
in D: through D and the centre 
C draw CD: the angle ACE will 
be equal to the angle ECB, and 
the arc AE to the arc EB. 


c 



V. Through a given point to draw a parallel to a given line , 

» 

52. Let A be the given point, and BC the given line. 

3 








84 


ELEMENTS OF SURVEYING. 


[BOOK 1 


From A as a centre, with a 
radius greater than the shortest 
distance from A to BC, describe 
the indefinite arc FD: from the 
•point E as a centre, with the same radius, describe the 
re AF; make ED — AF ) and draw AD: then will AD 
be the parallel required. 

YI. Two angles of a triangle being given , to find the third 

53. Draw the indefinite line 
DEF. At the point A, make 
the angle DEC equal to one of 
the given angles, and the angle 
CEII equal to the other: the re¬ 
maining angle HEF will be the 
third angle required. 




VII. To represent , on paper , a line of a given length , so that 
any number of its parts shall correspond to the unit of the 
scale. 

54. Suppose that the given line were 75 feet in length, 
and it were required to draw it on paper, on a scale of 25 
feet to the inch. 

The length of the line 75 feet, being divided by 25, 
will give 3, the number of inches which will represent the 
line on paper. 

Therefore, draw the indefinite line AB , on which lay 


off a distance AC equal to 3 inches: AC will represent 
the given line of 75 feet, drawn on the required scale. 

Remark I. This problem explains the manner of repre* 
enting a line upon paper, so that a given number of its 
parts shall correspond to the unit of the scale, whether 
that unit be an inch or any part of an inch. 

When the length of the line to be laid down is given,’ 
and it has been determined how many parts of it are to 







SEC. II.] GEOMETRICAL CONSTRUCTIONS 35 

♦ 

be represented on tlie paper by a distance equal to the 
unit of the scale, we find the length which is to be taken 
from the scale by the following 

RULE. 

Divide the length of the line by the number of parts which 
is to be represented by the unit of the scale: the quotient will 
show the number of units which is to be taken from the scale. 

EXAMPLES. 

1. If a line of 640 feet is to be laid down on paper, on 
a scale of 40 feet to the inch; what length must be taken 
from the scale ? 

40)640(16 inches. 

2. If a line of 357 feet is to be laid down on a scale 
of 68 feet to the unit of the scale, (which we will suppose 
half an inch), how many parts are to be taken ? 

Am. | 5 ' 25 P arts ’ or 
I 2.625 inches. 

3. A li ne of 3S4 feet is drawn on paper, on a scale of 
45 feet to the inch; what is its length on the paper ? 

Ans. 8.53 inches. 

Remark II. When the length of a line on the paper is 
given, and it is required to find the true length of the 
line which it represents, take the line in the dividers and 
apply it to the scale, and note the number of units, and 
parts of a unit to which it is equal. Then multiply this 
number by the number of parts which the unit of the 
scale represents, and the product will be the length of the 
line. 

For example, suppose the length of a line drawn on 
the paper was found to be 3.55 inches, the scale bc-mg 40 
feet to the inch: then, 

3.55 X 40 = 142 feet, the length of the line. 


f 


ELEMENTS OF SURVEYING. 


;[BOOX I. 


86 


VTLI. Having given two sides and the included angle of a iri • 

angle , to describe the triangle. 


55. Let th$ line B — 150 feet, and 0 = 120 feet, be the 
given sides; and A — 30 degrees, the given angle: to do 
scribe the triangle on a scale of 200 feet to the inch. 


©raw the indefinite line BG, and 
at the point IJ , make the angle GDH 
equal to 30 degrees: then lay off 
BG equal to 150, equal to three 
quarters of an inch, and Did equal 
to 120, equal to six tenths of an 
inch, and draw GH: BUG will be the required triangle. 



IX. The three sides of a triangle being given , to describe the 

triangle. 

56. Let A, B and OJ be the sides. 

Draw DE equal to the side A. 

From the .point D as a centre, with 
a radius equal to the second side B 1 
describe an arc: from E as a cen- . 
tre, with a radius equal to the third 
side (7, describe another arc inter¬ 
secting the former in F; draw BF and EF\ and BEE will 
be the triangle required. 



X. Having given two sides of a triangle and, an angle oppo¬ 
site one of them , to describe the triangle. 

57. Let A and B be the given sides, and 0 , the given 
angle, which we will suppose is opposite the side B. 

Draw the indefinite line BF 
and make the angle FBH equal to 
the angle 0: take BIT— X, from 
the point H, as a centre, with a 
jadius equal to the other given 
side, I?, describe an arc cutting 
T)F in F; draw TIE: then will BIIF be the required tri¬ 
angle. 














S E 0. II.] GEOMETRICAL CONST jfCJOTIONS. 

[f the angle C is acute, and 
the side B less than A , then 
the arc described from the 
centre E with the radius EF 
= B will cut the side BE in 
two points, F and G, lying on 
the same side of B: hence, there will be two triangles, 
BEF\ and BEG , either of which will satisfy all the condi¬ 
tions of the problem. 

XI. The adjacent sides of a parallelogram , with the omgle 
which they contain, being given , to describe the paral¬ 
lelogram. 

58. Let A and B be the given sides, and C the given 
angle. 

Draw the line BH , and 
lay off BE equal to A ; at 
the point D, make the angle 
EBF— G ; take BF — B: de¬ 
scribe two arcs, the one from 
F , as a centre, with a radius FG — BE ' the other from E, as 
a centre, with a radius EG — BF; through the point G, 
where these arcs intersect each other, draw FG , EG ; BEGF 
will be the parallelogram required. 

XII. To find the centre of a given circle or arc. 

59. Take three points, A , B , C\ any where in the cir¬ 
cumference, or in the arc: 
draw AB, BG; bisect these two 
lines by the perpendiculars, BE, 

FG: the point 0 , where these 
perpendiculars meet, will be the 
centre sought. 

O 

The same construction serves 
for making a circumference pass 
through three given points A, B, 

C, and also for describing a circumference, about a given 
triangle. 




^ - 

B \ --- 1 


C 


E 















38 


ELEMENTS OF SURVEYING. 


[BOOK L 


PLANE TBIG ONOMETBY. 

SECTION III. 

DEFINITIONS.—APPLICATION TO HEIGHTS AND DISTANCES, 

1. In every plane triangle there are six parts: three 
sides and three angles. These parts are so related to each 
other, that when one side and any two other parts are 
given, the remaining ones can be obtained, either by geo¬ 
metrical construction or by trigonometrical computation. 

2. Plane Trigonometry explains the methods of com¬ 
puting the unknown parts of a plane triangle, when a suf¬ 
ficient number of the six parts is given. 

3. For the purpose of trigonometrical calculation, the 
circumference of the circle is supposed to be divided into 
360 equal parts, called degrees; each degree is supposed 
to be divided into 60 equal parts, called minutes; and 
each minute into 60 equal parts, called seconds. 

Degrees, minutes, and seconds, are designated respec¬ 
tively, by the characters ° ' For example, ten degrees , 
eighteen minutes , and fourteen seconds , would be written 
10° 18' 14". 

4. If two lines be drawn through the centre of the 
circle, at right angles to each other, they will divide the 
circumference into four equal parts, of 90° each. Every 
right angle then, as EOA, is measured by an aj'c of 90°; 
every acute angle, as B6L4, by an arc less than 90°; and 
every obtuse angle, as FOA, by an arc greater than 90°. 

5. The complement of an arc is J 
what remains after subtracting the 
arc from 90°. Thus, the arc ED 
is the complement of AB. The 
sum of an arc and its complement $ 
is equal to 90°. 

6. The supplement of an arc is 
what remains after subtracting the 
arc from 180°. Thus, GF is the 












SEC. I.] 


PLANE TRIGONOMETRY 


39 


supplement of the arc AEE. The sum of an arc and its 
supplement is equal to 180°. 

7. The sine of an arc is the perpendicular let fall from 
one extremity, of the arc on the diameter which passes 
through the other extremity. Thus, BD is the sine of the 
arc AB. 

8. The cosine of an arc is the part of the diameter in¬ 
tercepted between the foot of the sine and centre. Thus, 
OB is the cosine of the arc AB. 

9. The tangent of an arc is the line which touches it at 
one extremity, and is limited by a line drawn through the 
other extremity and the centre of the circle. Thus, AC is 
the tangent of the arc AB. 

10. The secant of an arc is the line drawn from the 
centre of the circle through one extremity of the arc, and 
limited by the tangent passing through the other extremi¬ 
ty. Thus, OC is the secant of the arc AB. 

11. The four lines, BD, OB, AC, OC, depend for their 
values on the arc AB and the radius OA ; they are thus 
designated : 

sin AB for BD 
cos AB for OB 
tan AB for AC 
sec AB for OC 

12. If ABE be equal to a quadrant, or 90°, then EB 
will be the complement of AB. Let the lines ET and IB 
be drawn perpendicular to OE. Then, 

ET, the tangent of EB, is called the cotangent of AB; 

IB, the sine of EB, is equal to the cosine of AB; 

OT,\ the secant of EB, is called the cosecant of AB. 

In general, if A is any arc or angle, we have, 

cos A = sin (90° — ^1) 
cot A — tan (90° — A) 
cosec A = sec (90° — A) 


40 


ELEMENTS OF SURVEYING. 


[BOOR J 


13. If we take an arc, ABEF\ 
greater than 90°, its sine will be 
FlI; OH will be its cosine; AQ 
its tangent, and OQ its secant. 

But FH is the sine of the arc GF\ 
which is the supplement of AF, 
and Oil is its cosine; hence, the 
sine of an arc is equal to the sine of 
its supplement; and the cosine of an 
arc is equal to the cosine of its supplement* 

Furthermore, AQ is the tangent of the arc AF , and 
OQ is its secant: GL is the tangent, and OL the secant 
of the supplemental arc GF. But since AQ is equal to 
GL , and OQ to OL , it follows that, the tangent of an arc 
is equal to the tangent of its supplement; and the secant of av 
arc is equal to the secant of its supplement * 

TABLE OF NATURAL SINES. 

14. Let us suppose, that in a circle of a given radius, 
the lengths of the sine, cosine, tangent, and cotangent, have 
been calculated for every minute or second of the quad¬ 
rant, and arranged in a table; such a table is called a 
table of sines and tangents. If the radius of the circle is 
1, the table is called a table of natural sines. A table of 
natural sines, therefore, shows the values of the sines, co¬ 
sines, tangents, and cotangents of all the arcs of a quad¬ 
rant, which is divided to minutes or seconds' 

If the sines, cosines, tangents, and secants are known 
for arcs less than 90°,' those for arcs which are greater can 
be found from them. For if an arc is less than 90°, its 
supplement will be greater than 90°, and the numerical 
values of these lines are the same for an arc and its sup¬ 
plement. Thus, if we know the sine of 20°, we also know 
the sine of its supplement 160°; for the two are equal to 
each other. The Table of Natural Sines, beginning at page 
63. of the tables shows the values of the sines and cosines 
only. 

* These relations are between the numerical valueft of the trigonometrical lines; 
the algebraic signs, which they have in ti e different quadrants, are not considered. 


G 


















SEC. III.J 


PLANE TRIGONOMETRY. 


41 


TABLE OF LOGARITHMIC SINES. 

15. In this table are arranged the logarithms cf the 
numerical values of the sines, cosines, tangents, and co¬ 
tangents of all the arcs of a quadrant, calculated to a ra¬ 
dius of 10,000,000,000. The logarithm of this radius is 10. 
In the first and last horizontal lines of each page, are writ¬ 
ten the degrees whose sines, cosines, &c., are expressed on 
the page. The vertical columns on the left and right, are 
columns of minutes. 


CASE i. 

To find, in the table , the logarithmic sine, cosine, tangent , or 
cotangent of any given arc or angle. 

16. If the angle is less than 45°, look for the degrees 
m the first horizontal line of the different pages: when the 
degrees are found, descend along the column of minutes, on 
the left of the page, till you reach the number showing the 
minutes : then pass along a horizontal line till you come into 
the column designated, sine, cosine, tangent, or cotangent, as 
the case may be: the number so indicated is the logarithm 
sought. Thus, on page 37, for 19° 55', we find, 

sine 19° 55' ... . 9.582312 

cos 19° 55' ... . 9.973215 

tan 19° 55' ... . 9.559097 

cot 19° 55' ... . 10.440903 

17. If the angle is greater than 45°, search for the de¬ 
grees along the bottom line of the different pages : when the 
number is found, ascend along the column of minutes on the 
right hand side of the page, till you reach the number express¬ 
ing the minutes: then pass along a horizontal line into the 
column designated tang, cot, sine, or cosine, as the case may 
be: the number so pointed out is the logarithm required. 

18. The column designated sine, at the top of the page, 
is designated by cosine at the bottom; the one designated 
tang, by cotang, and the one designated cotang, by tang. 

The angle found by taking the degrees at the top of 
the page, and the minutes from the left hand vertical column, 
is the complement of the angle found by taking die degrees 


42 


ELEMENTS OF SURVEYING. 


[BOOK L 


at the bottom of the pag-3, and the minutes from the right 
hand column on the same horizontal line with the first. 
Therefore, sine, at the top of the page, should correspond 
with cosine, at the bottom; cosine with sine, tang \v ilh 
cotang, and cotang with tang, as in the tables (Art. 12). 

If the angle is greater than 90°, we have only to sub¬ 
tract it from 180°, and take the sine, cosine, tangent, or 
cotangent of the remainder. 

The column of the table next to the column of sines, 
and on the right of it, is designated by the letter D. 
This column is calculated in the following manner. 

Opening the table at any page, as 42, the sine of 24° 
is found to be 9.609313 ; that of 24° 01', 9.609597 : their 
difference is 284; this being divided by 60, the number 
of seconds in a minute, gives 4.73, which is entered in the 
column D. 

Now, supposing the increase of the logarithmic sine to 
be proportional to the increase of the arc, and it is nearly 
so for 60", it follows, that 4.73 is the increase of the sine 
for 1". Similarly, if the arc were 24° 20', the increase of 
the sine for 1", would be 4.65. 

The same remarks are applicable in respect of the 
column D , after the column cosine, and of the column D, 
between the tangents and cotangents. The column 21, be¬ 
tween the columns tangents and cotangents, answers to 
both of these columns. 

Now, if it were required to find the logarithmic sine 
of an arc expressed in degrees, minutes, and seconds, we 
have only to find the degrees and minutes as before; then, 
multiply the corresponding tabular difference by the sec¬ 
onds, and add the product to the number first, found, for 
the sine of the given arc. 

Thus, if we wish the sine of 40° 26' 28". 

The sine 40° 26' . . . 9.811952 

Tabular difference 2.47 . 

Number of seconds 28 . 

Product, 69.16 to be added 69.16 

Gives for the sine of 40° 26' 28". 9.812021. 





SEC. Ill 


PLANE TRIGONOMETRY. 


43 


The decimal figures at the right are generally omitted 
in the last result; but when they exceed five-tenths, the 
figure on lie left of the decimal point is increased by 1; 
the logarithm obtained is then exact, to within less than 
one unit of its right hand place. 

The tangent of an arc, in which there are seconds, is 
found in a manner entirely similar. ✓ In regard to the co¬ 
sine and cotangent, it must be remembered, that they in¬ 
crease while the arcs decrease, and decrease as the arcs are 
increased; consequently, the proportional numbers found 
for the seconds, must be subtracted, not added. 

% 

EXAMPLES. 

1. To find the cosine of 3° 40' 40". 

The cosine of 3° 40' . . . 9.999110 

Tabular difference .13 . 

Number of seconds 40 

Product, 5.20 to be subtracted 5.20 

Gives for the cosine of 3° 40' 40" 9.999105. 

2. Find the tangent of 87° 28' 31". 

Ans. 9.884592. 

3. Find the cotangent of 87° 57' 59". 

Ans. 8.550356. 


case ■ 

To find the degrees, minutes , and seconds answering to any 
given logarithmic sine , cosine, tangent, or cotangent. 

19. Search in the table, in the proper column, and 
if the number is found, the degrees will be shown either 
at the top or bottom of the page, and the minutes in the 
side column either at the left or right. 

But, if the number cannot be found in the table, take 
from the table the degrees and minutes answering to the 
nearest less logarithm, the logarithm itself, and also the 
corresponding tabular difference. Subtract the logarithm 
taken from the table from the g : ven logarithm, annex two 




44 


ELEMENTS OF SURVEYING. 


[BOOK L 


ciphers to the remainder, and then divide the remainder 

the tabular difference: the quotient will be seconds, 
and is to be connected with the degrees and minutes be¬ 
fore found: to be added for the sine and tangent, and 
subtracted for the cosine and cotangent. 

EXAMPLES. 

1. Find the arc answering to the sine 9.880054 
Sine 49° 20', next less in the table 9.879963 

Tabular difference, 1.81)91.00(50". 

Hence, the arc 49° 20' 50" corresponds to the given sine 
9.880054. 

2. Find the arc whose cotangent is 10.008688 
cot 44° 26', next less in the table 10.008591 

Tabular difference, 4.21)97.00(23". 

Hence, 44° 26' —23" = 44° 25' 87" is the arc answering 
to the given cotangent 10.008688. 

3. Find the arc answering to tangent 9.979110. 

Arts. 43° 37' 21". 

4. Find the arc answering to cosine 9.944599. 

Ans. 28° 19' 45". 

20. We shall now demonstrate the principal theorems 
of Plane Trigonometry. 


THEOREM I. 


The sides of a plane triangle are proportional to the sines of 

their opposite angles. 

21. Let ABC be a triangle; then will 

CB : OA : : sin A : sin B. 

For, with A as a centre, and AD 
equal to the less side BC\ as a ra¬ 
dius, describe the arc DT: and with 
B as a centre and the equal radius /L at l F t 
BO\ describe the arc CL , and draw DE and CF perpen¬ 
dicular to AB: now DE is the sine of the angle A, and 










SEC. 11L] 


PLANE TRIGONOMETRY. 


45 


OF is the sine of B , to the same radius AD or BC. But 
V similar triar gles, 

AD : DE : : : Cid 

But AD being equal to BC\ we have 

BC : sin A : : AC : sin B , or 

BC : AC : : sin X : sin B. 

By comparing the sides AB, AC, in a similar manner, 
we should find, 

AB : AC : : sin C : sin B. 


THEOREM II. 


In any triangle, the sum of the two sides containing either 
angle, is to their difference, as the tangent of half die sum of 
the two other angles, to the tangent of half their difference. 


22. Let ACB be a triangle: then will 


ABA-AC : AB— AC : : tan %(C+B) : tan \{C— B). 


With A as a centre, and a 
radius AC, the less of the two 
given sides, let the semicircumfe¬ 
rence IFCE be described, meeting 
AB in f and BA produced, in E. 

Then, BE will be the sum of the 
sides, and BT their difference. Draw Cl and AF. 

Since CAE is an outward angle of the triangle ACB, 



it is equal to the sum of the inward angles C and B (Bk. 
I., Prop. XXV., Cor 6). But the angle C1E being at the 
circumference, is half the angle CAE at the centre (Bk. 111., 
Prop. XVIII.); that is, half the sum of the angles C and 
B, or equal to \(CA-B). 

The angle AFC = ACB, is also equal to ABC+BAF; 
therefore, BAF= A CB- ABC 

But, ICF=l(BAF) = -l(ACB-ABC) J or \{C-B). 

With I and C as centres, and the common radius IC, 
let the arcs CD and IC be described, and draw the lines 
CE and III perpendicular to IC. The perpendicular CE 
will pass through E, the extremity of the diameter IE y 





46 


ELEMENTS OF SURVEYING. 


[BOOK L 


since the right angle ICE must be U 
inscribed in a semicircle. 

But CE is the tangent of CIE j \ / 

= and IH is the tan- \ \j / \\7 

gent of ICB=\[C— B), to the -. 

common radius CI. C"" . FGTf ^ 

But since the lines CE and III are parallel, the tri¬ 
angles Bill and BCE are similar, and give the proportion, 

BE : BI : : CE : IH, or 

by placing for BE and BI, CE and III, their values, we 
have * 

AB-\-AC : AB—AC :: tan \(C-\rB) : tan \{C—B). 


THEOREM III. 

* 

In any plane triangle, if a line is drawn from the vertical 
angle perpendicular to the base, dividing it into two segments: 
then, the ivhole base, or sum of the segments, is to the sum of 
the two other sides, as the difference of those sides to the differ - 
mcc of the segments. 

23. Let BA C be a triangle, and AD perpendicular to the 
base; then will 

BC : CA + AB :: CA-AB : CD-DB. 

For, AB 2 = ME + AD~ 

(Bk. IV., Prop. XI.); 

and AO' = DO* + AD 2 

-9 -2 

by subtraction, A C — AB~ = 

o — •—9 

CD' — B D . 

But since the difference of 
the squares of two lines is equivalent to the rectangle con¬ 
tained by their sum and difference (Bk. IV., Prop. X.), we 
have, 

AC 2 - AD : = (A 0+ AB). {A0- AB) 

and CD*-DB : = (CD + DB).{CD-DB) 

therefore, (CD + DB).{CD — DB) = (AC+ AB). (A C- AB) 
hence, CD -f DB : AC+AB :: AC— AB : CD—DR 


A 


















SEC. Ill] 


PLANE TRIGONOMETRY. 


THEOREM IY. 

fu any right-angled plane triangle, radius is to the tangent 
of either of the acute angles, as the side adjac mt to the side 
opposite. 

24. Let CAB be tbe proposed triangle, and denote the 
radius by R: then will 

Ji 

R : tan C : : AC : AB. 

\ 

For, with any radius as CD de¬ 
scribe the arc Dll] and draw the tan¬ 
gent DC. 

From the similar triangles CDG and CAB, we have, 

CD : DG : : CA : AB\ hence, 

R : tan C : : CA : AB. 

By describing an arc with B as a centre, we could 
show in the same manner that, 

R : tan B : : AB : AC. 

THEOREM V. 

In every right-angled plane triangle, radius is to the cosine 
of either of the acute angles, as the hypothenuse to the side 
adjacent. A % 

25. Let ABC be a triangle, right-angled at B: then will, 

R : cos A : : AC : AB. 

For, from the point A as a centre, 
with anv radius as AD, describe the 
arc DF, which will measure the angle 
A , and draw DE perpendicular to AB : then will AE be 
the cosine of A. 

The triangles ADE and ACB, being similar, we have, 

AD : AE : : AC : AB\ that is, 

R : cos A : : AC : AB. 

v 

Remark. The relations between the sides and angles 
of plane triangles, demonstrated in these five theorems, are 

J 










48 


ELEMENTS OF SURVEYING. 


[BOOK I 


sufficient to solve all the cases of Plane Trigonometry. 
Of the six parts which make up a plane triangle, three 
must be given, and at least one of these a side, before the 
others can be determined. 

If the three angles only are given, it is plain, that an 
indefinite number of similar triangles may be constructed, 
the angles of which shall be respectively equal to the 
angles that are given, and therefore, the sides could not be 
determined. 

Assuming, with this restriction, any three parts of a 
triangle as given, one of the four following cases will al¬ 
ways be presented. 

I. When two angles and a side are given. 

II. When two sides and an opposite angle are given. 

III. When two sides and the included angle are given. 

IY. AY hen the three sides are given. 


CASE i. 

When two angles and a side are given . 

26. Add the given angles together, and subtract their 
Sum from 180 degrees. The remaining parts of the tri¬ 
angle can then be found by Theorem I. 


EXAMPLES 




1. In a plane triAngle, 
there are given the angle A — 58° 07', 
the angle B~ 22° 87', and the side 
A B = 408 yards. Required the oth¬ 
er parts. 


c 



GEOMETRICALLY. 

27. Draw an indefinite straight line, AB, and from the 
scale of equal parts lay off AB equal to 408. Then, 
at, A, lay off an angle equal to 58° 07', and at B an angle 
equal to 22° 87', and draw the lines AC and BC: then 
will ABC be the triangle required. 

The angle C may be measured either with the protractor 
or the scale of chords (Sec. II., Arts. 42 and 44), and will be 

A 


4 




SEC III.] 


PLANE TRIGONOMETRY. 


49 


found equal to 99°, 16'. The sides AC and BC may be 
measured by referring them to the scale of equal parts 
(Sec. II., Art. 40). We shall find A 0— 158.9 and BC — 851 
yards. 


TRIGONOMETRICALLY BY LOGARITHMS. 

To the angle . . . A = 58° 07' 

Add the angle . . B — 22° 37' 

Their sum, =5-80° 44' * 

taken from . . . 180° 00' 

leaves C .... 99° 16', of which, as it ex¬ 

ceeds 90°, we use the supplement 80° 44'. 


To find the side BC. 

sin C 99° 16' ar. comp. 0.005705 

: sin A 58° 07'. 9.928972 

: : AB 408 . 2.610660 


: BC 351.024 (after rejecting 10) 2.545887. 

Remark. The logarithm of the fourth term of a pro¬ 
portion is obtained by adding the logarithm of the second 
term to that of the third, and subtracting from their sum 
the logarithm of the first term. But to subtract the first 
term is the same as to add its arithmetical complement 
and reject 10 from the sum (Sec. I., Art. 13) : hence, the arith¬ 
metical complement of the first term added to the loga¬ 
rithms of the second and third terms, minus ten, will give 
the logarithm of the fourth term. 

c 

To find the side AC. 


sin C 99° 16' ar. comp. 0.005705 
sin B 22° 37'. 9.584968 


AB 408 .. 2.610660 

AC 158.976 . 2.201838 


2. In a triangle ABC, there are given A — 33 J 25* 
Z? = 57° 42', and AB — 400 : required the remaining parts,. 

Ans C— 83° 53', BC= 249.974, AC— 340,04.. 

4 











60 


ELEMENTS OF SURVEYING. 


[BOOK 1 


CASE II. 

When two sides and an opposite angle are given. 


28. In a plane triangle, ABC, 
there are given A6 r = 216, CB =117, 
he angle A =22° 37', to find the 
other parts. 


c 



* GEOMETRICALLY. 

29. Draw an indefinite right line A BB' : from any 
point, as A, draw AC, making BAC= 22° 37', and make 
AC =213. With C as a centre, and a radius equal to 117, 
the other given side, describe the arc B'B\ draw B'C and 
BC : then will either of the triangles ABC or AB'C, an¬ 
swer all the conditions of the question. 


TRIGONOMETRICALLY. 


To find the angle B. 

BC 117 ar. comp. 7.931814 

: AC 216 . 2.334454 

: ; sin A 22° 37'.. . 9.584968 


• sin B 45° 13' 55", or ABC 134° 46' 05" 9.851236. 

The ambiguity in this, and similar examples, arises in 
consequence of the first proportion being true for either 
of the angles ABC, or ABC, which are supplements of 
each other, and therefore, have the same sine (Art. 13). 
As long as the two triangles exist, the ambiguity will con¬ 
tinue. But if the side CB, opposite the given angle, is 
greater than AC, the arc BB will cut the line ABB', on 
the same side of the point A, in but one point, and then 
there will be only one triangle answering the conditions. 

If the side CB is equal to the perpendicular Cd, the 
rc BB will be tangent to ABB, and in this case also 
there will be but one triangle. When CB is less than the 
perpendicular Cd, the arc BB will not intersect the base 
ABB, and in that case, no triangle can be formed, or it 
will be impossible to fulfil the conditions of the problem. 








SEC. Ill] 


PLANE .TRIGONOMETRY. 


51 


2. Given two sides of a triangle 50 and 40 respectively 
and the angle opposite the latter equal to 32° : required 
the remaining parts of the triangle. 

Arts. If the angle opposite the side 50 is acute, it is 
equal to 41° 28' 59"; the third angle is then equal to 
106° 31' 01", and the third side to 72.368. If the angle 
opposite the side 50 is obtuse, it is equal to 138° 31' 01", 
the third angle to 9° 28' 59", an d the remaining side to 
12.436. # 

CASE III. 

When the two sides and their included angle are given. 

30. Let ABO be a triangle; AB , 

BC, the given sides, and B the 
given angle. 

Since B is known, we can find 
the sum of the two other angles: 
for 

A+C= 180° - B, and, 
l(A 4- C) = i(180°-B). 

We next find half the difference of the angles A and 
0 by Theorem II., viz., 

BO+BA : BO—BA :: tan \{A+0) : tan \{A — C), 

in which we consider BO greater than BA, and therefore 
A is greater than 0\ since the greater angle must be op¬ 
posite the greater side. 

Having found half the difference of A and C ,J by add 
ing it to the half sum, |(ri 4- 0 ), we obtain the greater 
angle, and by subtracting it from half the sum, we obtain 
the less. That is, 

\{A + (7) T — (7) — A , and 
-}(A + 0) - i (A -0)=C 

Having found the angles A and C\ the third side AC 
nnay be found by the proportion, 

sin A : sin B : : BO : AC. 


A 




52 


ELEMENTS OF SURVEYING 


[BOOK L 


EXAMPLES. 

1. In the triangle ABC , let A (7 =540, AA = 450, and 
the included angle B = 80° : required the remaining parts. 

GEOMETRICALLY. 

\ \ 

31. Draw an indefinite right line BC\ and from any 
point, as B , lay off a distance B0= 540. At B make the 
angle CBA = 80° * draw BA, and make the distance 

D * A 7 W 

BA — 450 ; draw A C ; then will ABC be the required tri¬ 
angle. 


TRIG ONOMETRIC ALLY. 

BC+ BA = 540 + 450 = 990; and BC-BA = 540 - 450 = 90. 

A -f C = 180° — B — 180° — 80° = 100°, and therefore, 
J(A+ (7)=i(100°) = 50°. 


To find \{A — C). 

BCABA 990 ar. comp. 7.004365 

BO- BA 90 . 1.954243 

: tan J(A + CT) 50° . . 10.076187 

tan \{A -O) 6° 11'. 9.034795. 


Hence, 50° + 6° 11'= 56° 11' = A; and 50°-6° 11' = 
43° 49' = O. 


To find the third side AC. 

sin C ' 43° 49' ar comp. 0.159672 

. 9.993351 


sin B 


80° 


AB 450 


2.653213 


AO 640.082 . 2.806236. 

2. Given two sides of a plane triangle, 1686 and 960, 
and their included angle 128° 04': required the other parts. 
Ans. Angles, 33* 34'39"; 18° 21'21"; side 2400. 




CASE IV. 


32. Having given the three sides of a plane triangle, 
to find the angles. 


A 














SEC. Ill] 


PLANE TRIGONOMETRY. 


53 


Let fall a perpendicular from the angle opposite the 
greater side, dividing the given triangle into two right- 
angled triangles * then find the difference of the segments 
of the base by Theorem III. Half this difference being 
added to half the base, gives the greater segment; and, 
being subtracted from half the base, gives the less segment. 
Then, since the greater segment belongs to the righhangled 
triangle having the greater hypothenuse, we have two 
£ides and the right angle of each of two right-angled tri¬ 
angles, to find the acute angles.' 

EXAMPLES. 

1. The sides of a plane triangle 
being given ; viz., BC= 40, AC— 34, 
and AB = 25 : required the angles. 


A 



GEOMETRICALLY. 

83. With the three given lines as sides construct a tri¬ 
angle as in Prob. IX. Then measure the angles of the 
triangle either with the protractor or scale of chords. 


TRIGONOMETRICALLY. 


BG : AC+AB :: AC - AB : CD-BD, 


That is, 

40 

: 59 

: 59 X 9 _ 18 275 
40 

Then, 

40 +13.275 _ 
7 2 

= 26.6375 = CD, 

And, 

40- 

■ 13.275 _ 
2 

= 13.8625 = BD. 


In the triangle DAG.\ to find the angle DAG. 


‘AG 34 ar. comp. 8.468521 

DG 26.6375 . 1.425493 

sin D 90°. 10.000000 

in DA C 51° 34'40". 9.894014. 










54 


ELEMENTS OF SURVEYING. 


[BOOK I 


In the triangle BAD , to find the angle BAD. 


AB 25 ar. comp. 8.602060 

BD 13.3625 1.125887 

: sin D 90°. 10.000000 

sin BAD 32° 18' 35". 9.727947. 


Hence, 90° - DAC= 90° - 51° 34' 40" = 38° 25' 20" - <7, 
and, 90° - BAD = 90° - 32° 18' 35" = 57° 41' 25" - B, 
and, BAD + DAC= 51° 34' 40" + 32° 18' 35" = 83° 53' 

15" = A. 

2. In a triangle, of which the sides are 4, 5, and 6, 
what are the angles ? 

Ans. 41° 24' 35"; 55° 46' 16"; and 82° 49' 09" 


» SOLUTION OF RIGHT-ANGLED TRIANGLES. 

34. The unknown parts of a right-angled triangle may 
be found by either of the four last cases; or, if two of the 
sides are given, by means of the property that the square 
of the hypothenuse is equivalent to the sum of the squares 
of the two other sides. Or the parts may be found by 
Theorems IV. and V. 


EXAMPLES. 

1. In a right-angled triangle 
BAC, there are given the hypothe¬ 
nuse BC— 250, and the base AC — 
240 : required tLanother parts. 



BC 
AC 

; sin A 
sin B 

But (7=90° 


250 

240 


To find the angle B. 

ar. comp. 


7.6020' 
2.38r 


90°.10.01: 


73° 44' 23".9.9“ ; 


B = 90° - 73° 44' 23" = 16° 15' 



















S 6 C. Ill] 


PLANE TRIGONOMETRY. 


55 


Or 0 may be found from the proportion. 


CB 850 ar. comp. 7.602060 

AC 240 . 2.380211 

R . 10.000000 

cos C 16° 15' 37". 9.982271. 


« 

To find side AB by Theorem IV. 

R ar. comp. 0.000000 

tan C 16° 15' 37". 9.464889 

AC 240 . 2,380211 

AB 70.0003 . 1.845100. 


2. In a right-angled triangle BAG, there are given 
4(7=384, and B= 53° 08': required the remaining parts. 
Ans. AB= 287.96; BC= 479.979; C= 36° 52'. 


APPLICATION TO HEIGHTS AND DISTANCES. 

1. To determine the horizontal distance to a point which is ir&- 
accessible by reason of an intervening river A 

35. Let C be the point. Measure 
along the bank of the river a hori¬ 
zontal base line Mi?, and select the 
stations A and Z?, in such a man¬ 
ner that each can be seen from the 
other, and the point O from both 
of them. Then measure the hori¬ 
zontal angles CAB and 6 r Z?M, with 
an instrument adapted to that purpose. 

Let us suppose that we have found AB — 600 yards. 
CAB = 57° 35', and CBA = 64° 51'. 

The angle C= 180° - (A +B) = 57° 84'. 

To find the distance BC. 


sin C 57° 34' ar. comp. 0.073649 

sin A 57° 35'.. . . . 9.926431 

: AB 600 . 2.778151 

BC 600.11 yards. 2.778231. • 


* Read definitions, from 8 to 14, pages 64 and 65. 






































66 


ELEMENTS OF SURVEYING. 


[BOOK i 


To find the distance A G. 


sin G 67° 84' ar. comp. 0.073649 

sin B 64° 51'. 9.956744 

: AB 600 2.778151 

AG 643.94 yards. 2.808544 


II. To determine the altitude of an inaccessible object above a 

given horizontal plane. 


FIRST METHOD. 




36. Suppose 1) to be the inac¬ 
cessible object, and BG the hori¬ 
zontal plane from which the alti- ^ _ 

tude is to be estimated: then, if \/‘ / /\v 

we suppose DG to be a vertical 
line, it will represent the required 
distance. 

Measure any horizontal base line, as BA ; and at the 
extremities B and A , measure the horizontal angles GBA 
and GAB. Measure also the angle of elevation DBG. 

Then in the triangle GBA there will be known, two 
angles and the side AB: the side BG can therefore be 
determined. Having found BG, we shall have, in the 
right-angled triangle BBC, the base BG and the angle at 
the base, to find the perpendicular DG, which measures 
the altitude of the point D above the horizontal plane BG. 

Let us suppose that we have found 

174 = 780 yards, the horizontal angle GBA = 41° 24'; 
die horizontal angle GAB—9Q° 28', and the angle of eleva¬ 
tion DBC= 10°43'. 

In the triangle BGA, to find the horizontal distance BG 
The angle BGA = 180° - (41° 24' + 96° 28') = 42° 08' = G. 


sin G 42° 08' ar. comp. 0.173369 

: sin A 96° 28'. 9.997228 

: : AB 780 2.892095 

: BG 1155.29 . 3.062692. 













SEC. Ill] 


PLANE TRIGONOMETRY. 


57 


\ 


In the right-angled triangle BBC\ to find DC. 


R ar. comp. 0.000000 

tan DEC 10° 43'. 9.277043 

BC 1155.29 ...... / 3.062692 

DC 218.64 . 2.339735. 


Remark I. It might, at first, appear, that the solution 
which we have given, requires that the points B and A 
should be in the same horizontal plane; but it is entirely 
independent of such a supposition. 

For, the horizontal distance, which is represented by 
BA, is the same, whether the station A is on the same 
level with- B, above it, or below it. The horizontal angles 
CAB and CBA are also the same, so long as the point C 
is in the vertical line DC. Therefore, if the horizontal 
line through A should cut the vertical line DC, at any 
point, as E, above or below C, AB would still be the hori¬ 
zontal distance between B and A, and AE, which is equal 
to A C, would be the horizontal distance between A and C. 

If at A, we measure the angle of elevation of the point 
D, we shall know in the right-angled triangle DAE , the 
base AE, and the angle at the base; from which the per¬ 
pendicular DE can be determined. 

37. Let us suppose that we had measured the angle at 
elevation DAE\ and found it equal to 20° 15'. 

First: In the triangle BA C, to find A C or its equal AE. 


sin C 42° 08 ar. comp. 0.173369 

sin B 41° 24'. 9.820406 

: AB 780 2.892095 

AC 768.9 2.885870. 


In the right-angled triangle DAE\ to find DE. 

R ar. comp. 0.000000 

tan A 20° 15'. 9.566932 

: AE 768.9 . 2.885870 

DE 283.66 . 2.452802. 


X 




















58 ELEMENTS OF SURVEYING. [BOOK L 


Now, since BC is less than 


BE\ it follows that the station B 

I) 

is above the station A. That is, 


DE-DC= 283.66 - 218.64 = 

-B<fp - C 

65.02 = EC\ 

x / / E 

\ / ✓ ✓ -L-* 

\ / / ✓ 

\ / 

which expresses the vertical dis- 

\ _/W'"' 

tance that the station B is above 

V 

the station A. 



% 

Remark II. It should be remembered, that the vertical 
distance which is obtained by the calculation, is estimated 
from a horizontal line passing through the eye at the time 
of observation. Hence, the height of the instrument is to 
be added, in order to obtain the true result. 


SECOND METHOD. 



88. When the nature of the ground will admit of it, 
measure a base line AB in the direction of the object D. 
Then measure with the instrument the angles of elevation 
at A and B. 

Then, since the out¬ 
ward angle BBC is 
equal to the sum of 
the angles A and ABB, 
it follows that the an¬ 
gle ABB is equal to the difference of the angles Of eleva¬ 
tion at A and B. Hence, we can find all the parts of the 
triangle ABB. Having found BB, and knowing the angle 
BBC\ we can find the altitude DC. 

This method supposes that the stations A and B are on 
the same horizontal plane; and therefore it can only be 
used when the line AB is nearly horizontal. 

Let us suppose that we have measured the base line, 
and the two angles of elevation, and 


found 


requiisd the altitude DC. 


AB =975 yards, 
A = 15° 86', 
BBC = 27° 29'; 









8 E C. 111] 


PLANE TRIGONOMETRY. 


59 


First: ABB — BBC ~A = 27° 29' - 15° 36' = 11° 53'. 
In the triangle ABB\ to find BB. 


sin B 11° 53' ar. comp. 0.686302 

sin A 15° 36'. 9.429623 

AB 975 2.989005 

BB 1273.3 3.104930. 


In the triangle BBC\ to find BC. 

B ar. comp. 0.000000 

sin B 27° 29'. 9.664163 

BB 1273.3 3.104930 

DC 587.61 2.769093. 


III. To determine the perpendicular distance of an object below 

a given horizontal plane. 

39. Suppose C to be directly 
over the given object, and A the 
point through which the horizon¬ 
tal plane is supposed to pass. 

Measure a horizontal base line 
AB, and at the stations A and 
B conceive the two horizontal 
lines AC, BC, to be drawn. The 
oblique lines from A and B to the object are the hy- 
pothenuses of two right-angled triangles, of which AC, BO, 
are the bases. The perpendiculars of these triangles are 
the distances from the horizontal lines AC, BC, to the 
object. If we turn the triangles about their bases A G\ 
BC, until they become horizontal, the object, in the first 
case, will fall at C', and in the second at C". 

Measure the horizontal angles CAB, CBA , and also the 
angles of depression C'A C, C"B C. 



O v v 


V 


v . *v 
















60 


ELEMENTS OE SURVEYING. 


[E«'< K 1 


Let us suppose that we have 


/" 


found - 


AB = 672 yards 
BAG =72° 29' 

= 39° 20 


<?L16' = 27 0 49' 
G"BG— 19° 10'. 


First: in the triangle ABO, 
the horizontal angle A GB — 180° — {A 4- B) = 180° - 1 
49'= 68° 11'. 


a 


. To find the horizontal distance AC. 


sin C 68° 11' ar. comp. 0.03227.' 

sin B 89° 20'. 9.801978 

: AB 672 2.827369 

AC 458.79 2.661617 


To find the horizontal distance BC. 

sin C 68° 11' ar. comp. 0.082275 

sin A 72° 29'. 9.979380 

: AB 672 . 2.827869 

BC 690.28 ........ 2.839024. 


In the triangle GAG', to find CC'. 

R ar. comp. 0.000000 

: tan O'AC 27° 49'. 9.722815 

. : AC 458.79 . 2.661617 

: CC 242.06 ....... 2.383932. 


In the triangle CBC", to find CC"-. 

R ar. comp. 0.000000 

. tar. C"BC 19° 10'. 9.541061 

: : BC 690.28 . 2.839024 

: CC" 289.93 2.380085. 


Hence also, CC - CC" = 242.06 - 239.93 = 2.13 yards, 
which is the height of the station A above station B. 

























/ j 


& wWi?..' 


oEO. 1 H] 


‘VUtfcY'^ 1 v " I v 

i > i L ^ 

PLANE TRIGONOMETRY. 


PROBLEMS. 


Yv- 


61 



At 


A 

& r 

»•. 


1. Wanting to know tlie distance between two inacces¬ 
sible objects, which lie in a direct level line from the bot¬ 
tom of a tower of 120 feet in height, the angles of depres¬ 
sion ore measured from the top of the tower, and are found 
to be, of the nearer 57°, of the more remote 25° 80': re¬ 
quired the distance between the objects. 

1! ACOV'On WV lns - 173.656 feet. 

2. In order to find the distance 
between two trees, A and j 5, which 
could not be directly measured be¬ 
cause of a pool which occupied the 
intermediate space, the distances 
of a third point C from each of 
them were measured, and also the .' ; 
included angle ACB: it was found .ear/’ 

a 34 - r ' - *4>ft OB = 672 yhL 

, , , OA =588 yaM, ‘ 

*0 ACB- 55* 40! J 

required the distance A B. Ans. 522.967 yards. 

8. Being on a horizontal plane, and wanting to ascer¬ 
tain the height of a tower, standing on the top of an in¬ 
accessible hill, there were measured, the angle of elevation 
of the top of the hill 40°, and of the top of the tower 51®; 
then measuring in a direct line 1.80 feet farther from the 
hill, the angle of elevation of the top of the tower was 
83® 45'; required the height of the tower. 

Ans. 88.998. 



4. Wanting to know the hori¬ 
zontal distance between two inac¬ 
cessible objects E and IF, the fol¬ 
lowing measurements were made. 


viz. i 


AB = 536 yards 
BA W — 40 s 16' 
WAE=hV 40 
ABE =42° 22' 


required 


EBW =71° 07'; 
the di.‘Nance EW. 



Ans. 939.527 yards. 










62 




aafie i \\v< ^ ^ *\f 

' E L E0I E N T S OF SURVEYING. 



[BOOK i 


5. Wanting to know the 

O 

horizontal distance between 
two inacessible objects A 
and B, and not finding any 
station from which both of 
them could be seen, two 
points 0 and D, were chosen 
at a distance from each other, equal to 200 yards; from 
the former of these points A could be seen, and from the 
latter B , and at each of the points C and D a staff was 
set up. From C a distance CF was measured, not in the 
direction DC\ equal to 200 yards, and from D a distance 
VF equal to 200 yards, and the following angles taken, 

f AFC = 83° 00', BDF = 54° 30', 
viz. \ A CD = 53° 30', BDC = 156° 25', 

[ A CF = 54° 81', BED = 88° 80'. 

Ans. AB= 345.467 yards. 



6. From a station P there 

can be seen three objects, A , 

B and C, whose distances from 

each other are known: viz., 

AB~ 800, .4(7=600, and BC 

— 400 yards. Now, there are ; 

• < 

measured the horizontal an- 
gles. 

APC=Z?,° 45' and BPC 
= 22° SO': it is required to 
find the three distances PA, PC, and PB. 





PA = 710.193 yards. 
Ans. \PP = 1042.522" 

- [PB = 934.291. 


7. This * problem is much used in maritime survey¬ 
ing, for the purpose of locating buoys and sounding boats. 
The trigonometrical solution is somewhat tedious, but it 
may be solved geometrically by the following easy con¬ 
struction. iy 






‘ / 


/ / 


M 


o 


/* 

/, / 




SEC. Ill] 


V / 

PLANE TRIGONOMETRY 



63 


Let A , 2?, and C be the 
three fixed points on shore, 
and P the position of the 
boat from which the angles 
APC— 33° 45', CPB— 22° 30', 
and APB =66° 15', have been 
measured. 

Subtract twice APC =67° 

30' from 180°, and lay off at 
A and C two angles, CA 0 , 

A CO, each equal to half the 
remainder = 56° 15'. With 
the point 0 , thus determined, 
as a centre, and OA or OC as a radius, describe the cir¬ 
cumference of a circle: then, any angle inscribed in the 
segment APC\ will be equal to 33° 45'. 

Subtract, in like manner, twice CPB~A.h°, from 180°, 
and lay off half the remainder = 67° 30', at B and C, de¬ 
termining the centre Q of a second circle, upon the cir¬ 
cumference of which the point P will be found. The 
required point P will be at the intersection of these two 
circumferences. If the point P fall on the circumference 
described through the three points ^4, B, and C , the twc 
auxiliary circles will coincide, and the problem will be in 
determinate. 

i 

i : ■■ - ' x 

#r*m \ 






l 

\ v 
















BOOK II. 


PLANE SURVEYING. 


SECTION I, 

DEFINITION'S.—MEASUREMENT OF ANGLES AND LINES. 

1. Surveying, in its most extensive signification, com¬ 
prises all the operations necessary for finding, 

1st. The area or contents of any portion of the surface 
of the earth ; 

2d. The lengths and directions of the bounding lines; 
and, 

3d. For making accurate delineations of the surface and 
bounding lines on paper. 

It is divided into two branches, Plane and Geodesic 
Surveying. 

n rhe radius of the earth being very large, the curva¬ 
ture may be neglected, when the survey is limited to small 
portions of the surface. This branch is called Plane Sur¬ 
veying. 

When the curvature is taken into account, as it mu? 
be in all extensive surveys, the method of measurement 
and computation is called Geodesic Surveying. 

3. If at any point of the surface of the earth, regarded 
as a sphere, a plane be passed perpendicular to the radius, 
it will be tangent to the surface. Such a plane, and all 
planes parallel to it, are called horizontal planes. 

4. A plane perpendicular to a horizontal plane, at a 
given point, is called a vertical plane. 



eEU. 


DEFINITIONS, 


r "» 

J -j 


ii * 

b o 


5. A]] lines of horizontal planes are called horizontal 
lines. 

0. Lines which are perpendicular to a horizontal plane, 
are called vertical lines; and all lines which are inclined to 
it, are called oblique lines. 

Thus, AB and DC are hori¬ 
zontal lines; BC and AD are 
vertical lines; and A C and BD 
are oblique lines. 

7. The horizontal distance 
between two points, is the horizontal line intercepted be¬ 
tween the two vertical lines passing through those points. 
Thus, DC or AB is the horizontal distance between the two 
points A and (7, or the points B and D. 

8. A horizontal angle is one whose sides are horizxmtal; 
its plane is also horizontal. 

A horizontal angle may also be defined to be, the angle 
included between two vertical planes passing through the angular 
point, and the two objects which subtend the angle. 

9. A vertical angle is one, the plane of whose sides is 
vertical. 

10. An angle of elevation , is a vertical angle having one 
of its sides horizontal, and the inclined side above the hor¬ 
izontal side. 

Thus, in the last figure, BAG is the angle of elevation 
from A to C. 

11. An angle of depression , is a vertical angle having 
one of its sides horizontal, and the inclined side under the 
horizontal side. Thus, DC A is the angle of depression 
from C to A. 

12. An oblique angle is one, the plane of whose sides is 
oblique to a horizontal plane. 

13. All lines, which can be the object of measurement,, 
must belong to one of thf classes above named, viz.: 

1st. Horizontal lines: 

2d. V ertical lines : 

3d. * Oblique lines. 

5 



\ 



6 6 ELEMENTS OF SURVEYING. [BOOK II 

14. All the angles may also be divided into three 
classes, viz.: 

1st. Horizontal angles: 

2d. Vertical angles; which include angles of elevation 
an 1 angles of depression : and 

t 

3d. Oblique angles, or those included by oblique lines. 


OF THE MEASUREMENT OF LINES AND ANGLES. 

^ 15. It has been shown (Bk. I., Sec. III., Art. 1), that at 

least one side and two of the other parts of a plane triangle 
must be given or known, before the remaining parts can 
. be found by calculation. 

When, therefore, distances are to be found, by trigono- 
metrical calculations, two preliminary steps are necessary : 

1st. To measure certain lines on the ground : 

2d. To measure such angles as may be necessary to de¬ 
termine the required parts. 


MEASURES FOR DISTANCES. 

• 16. Any tape, rod, or chain, divided into equal parts, 

may be used as a measure; and one of these equal parts 
is called the unit of the measure. The unit of a measure 
may be a foot, a> yard, a rod, or airy other ascertained 
distance. 

The measure in general use, is a chain of four rods oi 
sixty-six feet in length; it is called Gunter’s chain, from 
the name of the inventor. This chain is composed of 100 
links. Every tenth link from either end, is marked by a 
small attached brass plate, which is notched, to designate 
its number from the end. The division of the chain into 
100 equal parts, is a very convenient one, since the divi¬ 
sions or links are decimals of the whole chain, and*in the 
calculations may be treated as such. 


SEC L] MEASUREMENT OF DISTANCES. 


67 


TABLE. 

1 chain = 4 rods = 66 feet =792 inches = 100 links. 
Hence, 1 link is equal to 7.92 inches. 

80 chains = 320 rods = 1 mile. 

40 chains = \ mile. 

20 chains = J mile. 

17. Besides the chain, there are needed for measuring:, 
ten marking pins, which should he of iron, each about ten 
inches in length and an eighth of an inch in thickness. 
These pins should be strung upon an iron ring, and this >. 
ring should be attached to a belt, to be passed over the* 
right shoulder, suspending the pins at the left side. Two 
staves are also required. Each of these should be about six 
feet in length, and have a spike in the lower end to aid in 
holding it firmly, and a horizontal strip of iron to pre¬ 
vent the chain from slipping off; these staves are to be 
passed through the rings at the ends of the chain. 

TO MEASURE A HORIZONTAL LINE. 

18. At the point where the measurement is to be be¬ 
gun, place, in a vertical position, a signal staff, having a 
small flag attached to its upper extremity; and place an¬ 
other at the point where the measurement is to be termi¬ 
nated. These two points are generally called stations , 

Having passed the staves through the rings of the 
chain, let the ten marking pins and one end of the chain • 
be taken by the person who is to go forward, and who is 
called the leader, and let him plant the staff as nearly as 
possible in the direction of the stations. Then, taking the 
staff in his right hand, let him stand off at arm’s length, 
so that the person at the other end of the chain can align 
it exactly with the stations: when the alignment is made, 
let the chain be stretched and a marking pin placed; then 
measure- a second chain in the same manner, and so on, 
until all the marking pins shall have been placed. When 
the marking pins are exhausted, a note should be made, 
that ten chains have been measured; after which, the 
marking pins are to be returned to the leader, and the 


63 ELEMENTS OF SURVEYING. [BOOK II. 

measurement continued as before, until the whole distance 
is passed over. It will be found desirable to fasten pieces 
of red cloth to the heads of the marking pins, that they 
may be more readily found in thick grass, brushwood, &c. 

Great care must be taken to keep the chain horizontal, 
and if the slope of the ground be too great to admit of 
measuring a whole chain at a time, a part of a chain only 
should be measured: the sum of all the horizontal lines so 
measured, is evidently the horizontal distance between the 
stations. 

For example, in measuring 
the horizontal distance between 
A and C, we first place a staff ' 
at A and another at b, in the 
direction towards C. Then 
slide up the chain on the staff 
at A until it becomes horizon¬ 
tal, and note the distance ab. 

Then remove the staves “and place them at b and d: make 
the chain horizontal, and note the distance cd. Measure 
in the same manner the line fC ; the sum of the horizontal 
lines ab , cd, fC, is equal to AB, the horizontal distance be¬ 
tween A and C. 

19. The length of the chain should be compared, from 
time to time, with a standard kept for the purpose. 

To facilitate this comparison, let two stakes be driven 
in the ground, distant from each other one chain , and let 
nails be driven in the heads of the stakes to mark the ex 
act length of the standard. 

Marks made upon the coping of a wall will answer the 
same purpose. If it is found that any line has been mea¬ 
sured with a chain, either too short or too long, the mea¬ 
sured distance may be corrected by the following pro¬ 
portion : 

As the length of the chain 
: the length of the standard 

: : the measured distance 
: tie true distance. 













SEC. I] 


OF TII E THEODOLITE 


69 


For tlie correction of areas we have this proportion, 

As the square of the length of the chain 

: the square of the length of the standard, 

: : the area found 

: the area required. 


MEASUREMENT OF ANGLES. 

} 

20. We come now to the measurement of angles, and 
for this purpose several instruments are used. The one, 
however, which affords the most accurate results, and which 
indeed can alone he relied on for nice or extensive opera¬ 
tions, is called a Theodolite. This instrument only will be 
described at present; others will be subsequently explained. 


OF THE THEODOLITE. 


PI. 1. The theodolite is an instrument used to measure 
horizontal and vertical angles. It is usually placed on a 
tripod ABC, which* enters by means of a screw the lower 
horizontal plate EE, and becomes firmly attached to the 
body of the instrument. Through the horizontal plate EE, 
four small hollow cylinders are inserted, which receive 
four screws with milled heads, that work against a second 
horizontal plate, EG. The upper side of the plate EE 
terminates in a curved surface, which encompasses a ball, 
that is nearly a semi-sphere, with the plane of its base 
horizontal. This ball, which is hollow, is firmly connected 
with the smaller base of a hollow conic frustum, that 
passes through the curved part of the plate EE\ and 
screws firmly into the curved part of the second horizontal 


plate EG. 

A hollow conic spindle passes through the middle of 
the ball, and the hollow frustum with which it is connect¬ 
ed. To this spindle, a third horizontal and circular plate 
HI, called the limb of the instrument, is permanently attached. 
Within this spindle, and. concentric with it, there is a sec¬ 
ond spindle, called the inner, or solid spindle. To this 
latter, is united a thin circular plate, called the vernier plate , 


70 ELEMENTS OF SURVEYING. [BOOK II 

which, rests on the limb of the instrument, and supports 
the upper frame-work. The two spindles terminate at the 
base of the spherical ball, where a small screw enters the 
inner one, and presses a washer against the other, and the 
base of the ball. On the upper surface of the plate FG, 
rests a clamp which goes round the outer spindle, and 
which, being compressed by the clamp-screw K, is made 
fast to it. This clamp is thus connected with the plate 
FG. A small cylinder a, is fastened to the plate FG : 
through this cylinder a thumb-screw L passes, and works 
into a small cylinder b, connected with the clamp. The 
cylinders b and a , admit of a motion round their axes, to 
relieve the screw I of the pressure which would otherwise 
be occasioned by working it. 

Directly above the clamp, is the lower telescope MN. 
This telescope is connected with a hollow cylinder, which 
is worked freely round the outer spindle, by the thumb¬ 
screw P having a pinion working into a concealed cog¬ 
wheel, that is permanently fastened to the limb of the in¬ 
strument By means of a clamp-screw Q, the telescope is 
made fast to the limb, when it will have a common motion 
with the limb and outer spindle. 

The circular edge of the limb is chamfered, and is gen 
erally made of silver, and on this circle the graduation for 
horizontal angles is made. In the instrument described, 
the circle is cut into degrees and half degrees; the degrees 
are numbered from 0 to 360. 

On the circular edge of the vernier plate, is a small 
plate of silver, called a vernier; this plate is divided into 
30 equal parts, and numbered from the line marked 0 to 
the left. Two levels, at right angles to each other, are 
attached to the vernier plate by small adjusting screws; 
one of the levels is seen in the figure. 

The vernier plate turns freely around with the inner 
spindle. It is made fast to the limb of the instrument by 
the clamp-screw S ; after which the smaller motions are 
made by the tangent-screw T. There is a compass on the 
vernier plate, that is concentric with it, the use of which 
will be explained under the head compass. 


SEC. L] 


OF THE THEODOLITE. 


71 


The frame-work which supports the horizontal axis of 
the vertical semicircle UV and the upper telescope, with 
its attached level, rests on the vernier plate, to which it 
is made fast by three adjusting screws, placed at the angu¬ 
lar points of an equilateral triangle. The vertical semi¬ 
circle UV, is called the vertical limb ; its motions are gov¬ 
erned by the thumb-screw Z ’ which has a pinion, that 
works with the teeth of the vertical limb. On the face 
of the vertical limb, opposite the thumb-screw Z, the limb 
is divided into degrees and half degrees: the degrees are 
numbered both ways from the line marked 0. There is a 
small plate resting against the graduated face of the verti¬ 
cal limb, called the vernier; it is divided into 30 equal 
parts, and the middle line is designated by 0. 

On the other face of the vertical limb, are two ranges 
of divisions, commencing at the 0 point, and extending 
each way 45°. The one shows the vertical distance of 
any object to which the upper telescope is directed, above 
or below the place of the instrument, in 100th parts of the 
horizontal distance: the other, the difference between the 
hypothenusal and base lines: the hypothenuse being sup¬ 
posed to be divided into one hundred equal parts: there¬ 
fore, by mere inspection, we can ascertain the number of 
links, which must be subtracted from every chain of an 
oblique line, to reduce it to a true horizontal distance. 

The supports .of the upper telescope are called the 
wyes, and designated Y's. Two loops, turning on hinges, 
pass over the telescope, and are made fast by - the pins c 
and d ; these loops confine the telescope in the Y's. By 
withdrawing the pins, and turning the loops on their 
hinges, the telescope may be removed for the purpose of 
being reversed in position; and in both situations, the tele¬ 
scope can be revolved in the Y's about its axis. 

In the telescopes attached to the theodolite, are two 
principal lenses, one at each end. The one at the end 
where the eye is placed, is called the eye-glass, the other 
the object-glass 

In order that the axis of the telescope may be directed 
to an object with precision, two spider’s lines, or small 


72 


[BOOK II 


ELEMENTS OF SURVEYING. 

hairs, are fixed at right angles to each other, and placed 
within the barrel of the telescope, and at the focus of the 
eye-glass. The vertical hair is moved by two small hori¬ 
zontal screws, one of which, f is seen in the figure; and 
the horizontal hair, by two vertical screws, g and h. 

Before using the instrument it must be adjusted , that is, 
the parts must be brought to their proper relative positions : 
there are four principal adjustments. 

First adjustment. — To fix the intersection of the spider } s 
lines in the line of collimation or axis of the telescope. 

Having screwed the tripod to the instrument, extend 
the legs, and place them firmly. Then loosen the clamp- 
screw jS of the vernier plate, and direct the telescope to a 
small, well-defined, and distant object. By means of a 
small pin f, on the under side of the telescope, slide the 
eye-glass till the spider’s lines are seen distinctly ; then with 
the thumb-screw AT, which forces out and draws in, the 
object-glass, adjust this glass to its proper focus, when the 
object, as well as the spider’s lines, will be distinctly seen: 
after which, by the tangent-screw T and the thumb-screw 
Z, bring the intersection of the spider’s lines exactly upon 
a well-defined point of the object. 

Having done this, revolve the telescope in the Y’s half 
round, when the attached level mn, will come to the upper 
side. See, in this position, if the horizontal hair appears 
above or below the point, and in either case, loosen one, 
and tighten the other, of the two screws that work the 
horizontal hair, till the horizontal hair has been carried 
over half the space between its last position and the ob¬ 
served point. Carry the telescope bade to its place ; di¬ 
rect again the intersection of the spider’s lines to the point, 
and repeat the operation till the horizontal hair neither 
ascends nor descends, while the telescope is revolved. A 
similar process will arrange the vertical hair, and the line 
of collimation is then adjusted. 

Second adjustment. — To malce the axis of the attached 
level of the upper telescope , parallel to the line of collimation. 

Turn the vernier plate, till the telescope comes directly 


SEC. I] 


OF THE THEODOLITE. 


73 


over two of tlie levelling 1 screws, between the plates DE 
and FG. Turn these screws contrary ways, keeping them 
firm against the plate FG , till the bubble of the level mw, 
stands at the middle of the tube. Then, open the loops, 
and reverse the telescope. If the bubble still stands in the 
middle of the tube, the axis of the tube is horizontal; but 
if not, it is inclined, the bubble being at the elevated end. 
In that case, by means of the small vertical screws m and 
n, at the ends of the level, raise the depressed end, or de¬ 
press the elevated one, half the inclination; and then, with 
the levelling screws, bring the level into a horizontal posi¬ 
tion. Eeverse the telescope in the Y’s, and make the 
same correction again; and so on, until the bubble stands 
in the middle of the tube, in both positions of the tele¬ 
scope : the axis of the level is then horizontal. Let the 
telescope be now revolved in the YU. IF the bubble con¬ 
tinue in the middle of the tube, the axis of the level is 
not only horizontal, but also parallel to the line of colli- 
mation. If, however, the bubble recede from its centre, 
the axis of the level is inclined to the line of collimation, 
and must be made parallel to it by means of two small 
antagonistic screws, (one of which is seen at p,) which work 
horizontally. By loosening one of them, and tightening 
the other, the level is soon brought parallel to the line of 
collimation, and then, if the telescope be revolved in the 
Y's, the bubble will continue in the middle of the tube. 

It is difficult to make the first part of this adjustment, 
while the axis of the level is considerably inclined to the 
line of collimation; for, if the level were- truly horizontal 
in one position of the telescope, when the telescope is re¬ 
versed, the bubble would not stand in the middle of the 
tube, except in one position of the level. This suggests 
the necessity of making the first part of the adjustment 
with tolerable accuracy; then, having made the second 
with care, let the first be examined, and proceed thus till 
the adjustment is completed. 

Third adjustment. —To make the axes of the levels on 
the Ural) perpendicular to t\e axis of the instrument. 

This adjustment is effected, partly by the levelling 


74 


ELEMENTS OF SURVEYING [BOOK IJ 


screws, and partly by tlie thumb-screw Z. Turn the ver¬ 
nier plate, until the upper telescope comes directly over 
two of the levelling screws, then turn them contrary ways, 
till the upper telescope is horizontal; after which, turn the 
vernier plate 180°, and if the bubble of the level remains 
in the middle of the tube, one line of the limb is horizon ■ 
tal. But if the bubble recede from the centre of the level, 
raise the lower, or depress the upper end, one-half by the 
levelling screws, the other by the thumb-screw Z , till it is 
brought into a horizontal position. Turn the vernier plate 
again 180°, and if the level be not then horizontal, make 
it so, by dividing the error as before, and repeat the op¬ 
eration until the line of the limb is truly horizontal. 
Then turn the vernier plate 90°, and level as before. 
The limb ought now to be truly horizontal; but lest the 
first horizontal line may have been changed, in obtaining 
the second, it is well to bring the telescope and level two 
or three times over the levelling screws, until an. entire 
revolution can be made without displacing the bubble from 
the middle of the tube. As this can only be the case 
when the level revolves around a vertical line, it follows 
that the limb will then be horizontal, and the axis of the 
instrument vertical. Then, by means of the small screws at 
the ends of the levels, bring the bubbles to the centres, and 
the axes of the levels will then be perpendicular to the axis 
of the instrument. 

Fourth adjustment. — To make the axis of the vertical 
limb perpendicular to the axis of the instrument. 

Bring the intersection of the spider's lines of the upper 
telescope upon a plumb line, or any well-defined vertical 
object,- and move the telescope with the thumb-screw Z: 
if the intersection of the spider’s lines continue on the ver¬ 
tical line, the axis is horizontal. 

Or, the adjustment may be effected thus: Direct the 
intersection of the spider’s lines to a well-defined point 
that is considerably elevated : then turn the vertical limb, 
until the axis of the telescope rests on some other well-de¬ 
fined point, upon or near the ground: reverse the tele¬ 
scope, and turn the vernier jfiate 180°; now, if in elevating 
and aep.xjsing the telescope, the line of collimation passes 


SEC. I.J 


VERNIERS. 


75 


through the two points before noted, the axis is horizontal. 
If it be found, by either of the above methods, that the 
axis is not horizontal, it must be made so bv the screws 
which fasten the frame-work to the vernier plate. 

There are two important lines of the theodolite, the po¬ 
sitions of which are determined with great care by the 

maker, and. fixed permanently. First, the axis of the in¬ 

strument is placed exactly at right angles with the limb 
and vernier plate; and unless it have this position, the 
vernier plate will not revolve at right angles to the axis, 
as explained in the third adjustment. Secondly, the line 
of collimation of the upper telescope is fixed at right angles 
to the horizontal axis of the vertical limb. We can as¬ 
certain whether these last lines are truly at right angles, 

by directing the intersection of the spider’s lines to a well- 
defined point; then removing the caps which confine the 
horizontal axis in its supports, and reversing the axis : if 
the intersection of the spider’s lines can be made to cover 
exactly the same point, without moving the vernier plate, 
the line of collimation is at right angles to the axis. 

If the theodolite be so constructed that either of the 
JT’s admits of being moAmd laterally, so as to wary the 
ancle between the horizontal axis and. the line of collima- 
tion, these lines may be adjusted at right angles to each 
other, if they have not been so placed by the maker. 

The lower telescope being used merety as a guard, re¬ 
quires no adjustment, although it is better to make the 
axis, about which its vertical motions are performed, hori¬ 
zontal, or perpendicular to the axis of the instrument; and 
this is easily effected by means of the two small screws k 
and Z, which work into the slide A', that is connected with 
the horizontal axis. 

Having explained the methods of properly adjusting the 
theodolite, we will now explain the particular uses of its 
several parts, and the manner of measuring angles. 


VERNIERS. 

21. Before explaining the vernier, ns applied to the tne 
odoliff, we shall discuss the general theory of verniers. 


76 


ELEMENTS OF SURVEYING. [BOOK IL 


A Vernier is a contrivance for measuring parts of the 
equal spaces marked off on a given scale or limb. 

It is a graduated scale, so arranged, as to cover an ex¬ 
act number of equal spaces on the primary scale or limb , 
to which it is applied. It is divided into a number of 
equal parts, greater by one than the number of equal spaces 
which it covers on the limb. 

The vernier may be applied to any scale of equal parts. 
The modes of its application are extremely various; the 
principle, however, is the same in all, and may be illus- 
trated by a simple diagram. 


8 ,0 JO 11 12 13 11 JJ 16 17 is 19 














c 

1 


1 

JJ 


0 1234-66789 10 


Let AB be any limb or scale of equal parts, one of 
which let us suppose equal to b. Let Cl) be a vernier , 
equal in length to nine of these parts, and itself divided 
into ten equal spaces, each one of which is then equal to 
nine-tenths of b. The difference between a space on the 
limb and a space on the vernier, is therefore equal to one- 
tenth of b or This is the least space that can be meas¬ 

ured by means of the vernier, and is called the least count; 
hence, 

The least count of a vernier is equal to one of the equal 
divisions of the limb divided by the number of spaces on the 
vernier. 

22. The true reading of the instrument, for any position 
of the vernier, expresses the distance from the point where 
the graduation on the limb begins, marked 0, to the 0 
point of the vernier. In the diagram, that distance is ex¬ 
pressed by nine units of the scale, or 9. 

If, now, the vernier be moved till the division 1 coin¬ 
cides with the division 10 of the limb, the 0 point will 
have advanced along the limb a distance equal to 
and the reading will become 9 + f 6 b. If we again 
move the vernier till the division 2 coincides with the di¬ 
vision 11 of the scale, the 0 point will have advanced an 
additional distance,' equal to T y>, and the reading becomes 























SEC. LJ 


MEASUREMENT OF ANGLES. 


77 


9 -t* j T) b ; when 3 coincides with division 12, the reading 
will become 9 + anc ^ so OT b till finally, when the point 

10 coincides with 19 of the scale, the distance 9 will have 
been increased by \%b, and will become 10, as it should, 
since, in that case, the 0 point will have been moved a whole 
space, and will coincide with the division 10 of the limb. 
Hence, the following rule for reading an instrument which 
has a vernier. 

Read the limb in the direction of the graduation up to the 
division line next preceding the 0 point of the vernier ; this 
is called the reading on the limb. Look along the vernier till 
a dividing line is found to coincide with a line of the limb: 
multiply the number of this first line by the least count of the ver¬ 
nier : this is the reading on the vernier: the sum of these two 
readings is the reading of the instrument. 

23. In the theodolite described, the limb is divided into 
half degrees, and 30 spaces on the vernier cover 29 spaces 
on the limb. Hence, the least count of this instrument is 
p of a half degree or 1'. Fig. 2, Plate 1, exhibits the 
vernier of the horizontal limb, and Fig. 3 the vernier of 
the vertical limb. 

TO MEASURE A HORIZONTAL ANGLE WITH THE THEODOLITE. 

24. Place the axis of the instrument directly over the 
point at which the angle is to be measured. This is ef¬ 
fected by means of a plumb, suspended from the plate 
which forms the upper end of the tripod. 

Having made the limb truly level, place the 0 of the 
vernier at 0 or 360° of the limb, and fasten the clamp- 
screw S of the vernier plate. Then, facing in the direc¬ 
tion between the lines which subtend the angle to be mea¬ 
sured, turn the limb with the outer spindle, until the tele¬ 
scope points to the object on the left, ver}^ nearly. Clamp 
the limb with the clamp-screw If and by means of the 
tangent screws L and Z , bring the intersection of the 
spider’s lines to coincide exactly with the object. 

Having loosened the clamp-screw Q of the lower tele¬ 
scope MN, direct it with the thumb-screw P to the 


73 


ELEMENTS OF SURVEYING. 


[BOOK II. 


same object at which the upper telescope is directed ; then 
tighten the clamp-screw Q. This being done, loosen the 
clamp-screw S of the vernier plate, and direct the telescope 
to the other object: the arc passed over by the 0 point 
of the vernier, is the measure of the angle sought. 

The lower telescope having been made fast to the limb, 
will indicate any change of the position of the limb, should 
any have taken place; and, as the accuracy of the mea¬ 
surements depends on the fixedness of the limb, the lower 
telescope ought to be often examined, and if its position has 
been altered, the limb must be brought back to its place by 
the tangent-screw L. 

It is not necessary to place the 0 point of the vernier 
at the 0 point of the limb, previously to commencing the 
measurement of the angle, but convenient merely; for, 
whatever be the position of this point on the limb, it is 
evident that the arc which it passes over is the true mea¬ 
sure of the horizontal angle. If, therefore, its place be 
carefully noted for the first direction, and also for the sec- 
ond, the difference of these two readings will be the true 
angle, unless the 0 point of the vernier shall have passed 
the 0 point of the limb, in which case the greater reading 
must be subtracted from 360°, and the remainder added to 
the less. 


TO MEASURE A VERTICAL ANGLE. ‘ 

25. We shall first explain the method of determining 
the index error. Having levelled the horizontal limb, di¬ 
rect the telescope to some distinctly marked object as the 
top of a chimney, and read the instrument. Reverse the 
telescope in the Ws, and turn the vernier plate 180°, and 
having directed the telescope to the same object, again 
read the instrument. If the two readings are the same, 
the limb is adjusted; that is, the 0 of the limb coincides 
with the 0 of its vernier, when the axis of the telescope 
is parallel to the horizontal limb. 

When the reading found with the eye end of the tele¬ 
scope nearest the vernier, is gieater than that obtained in 
the reversed position, the true elevation of the object 


SEC I] 


PRACTICAL PROBLEMS. 


79 


which, is equal to a mean of the readings, may be obtained 
by subtracting half their difference from the first reading. 
If the first reading is less than the second, the half differ¬ 
ence must be added to the first: Hence, 

To find the index error , take the reading of the limb when 
the telescope is directed to a fixed object, first with the eye end 
of the telescope nearest the vernier , and then luith the telescope 
and vernier plate both reversed. Take half the difference of 
these readings , and affect it with a minus sign if the first is 
greater, or a plus sign if the second is the greater; this is equal 
to the index error. 

Let the operation be repeated several times, using dif¬ 
ferent objects, and a mean of the errors will be more cor¬ 
rect than the result of a single observation. 

26. Having determined the index error, let the axis of 
the telescope be directed to any point either above or be¬ 
low the plane of the limb, and read the are indicated by 
the 0 of the vernier. To the arc so read apply the proper 
correction, if any, and the result will be the true angle of 
elevation or depression. 

The angle of elevation may be more correctly found by 
taking the elevation of the object, and repeating the obser¬ 
vation with the telescope and vernier plate reversed, and 
then taking a mean, of the readings for the angle required. 

MEASUREMENTS WITH THE TAPE OR CHAIN ONLY. 

27. It often happens that instruments for the measur 
ment of angles cannot be easily obtained; we must then 
rely entirely on the tape or chain. 

We now propose to explain the best methods of deter¬ 
mining distances, without the aid of instruments for the 
measurement of horizontal or vertical angles. 

I. To trace , on the ground , the direction of a right line , that 

shall be perpendicular at a given point , to a given right 

line. 

FIRST METHOD. 

28. Let BC be the given right line, and A the given 


80 ELEMENTS OF SURVEYING. [BOOK IJ. 

point. Measure from A, on the 
line BO\ two equal distances AB, 

AC, one on each side of the point 
A. Take a portion of the chain 
or tape, greater than AB, and 
place one extremity at B, and with the other trace the arc 
of a circle on the ground. Then remove the end which 
was at B, to C, and trace a second arc intersecting the 
former at 1). The straight line drawn through B and A 
will be perpendicular to BC at A. 


D 

t 


B 


A 


SECOND METHOD. 


29. Having made AB — A C, take 
any portion of the tape or chain 
considerably greater than the dis¬ 
tance between B and G. Mark 
the middle point of it, and fasten 
its two extremities, the one at B 
and the other at C. Then, taking the chain by the middle 
point, stretch it tightly on either side of BC\ and place a 
staff at D or E : DAE will be the perpendicular re¬ 
quired. 


D 



THIRD METHOD. 


30. Let AB be the given line, 
and C the point at which the per¬ 
pendicular is to be drawn. From 
the point C measure a distance CA 
equal to 8. With C as a centre, 
and a radius equal to 6, describe 
an arc on either side of AB : then, 


A 


X 


c 


j} 


B 


with A as a centre, and a radius equal to 10, describe a 
second arc intersecting at E , the one before described: 
then draw the line EC, and it will be perpendicular to 
AB at C. 


Remark. Any three lines, having the ratio of 6, 8, and 
10, form a right-angled triangle, of which the side corre^ 
spending to 10 is the hvpothenuse. 








6 EC. i.J 


SURVEYING- CROSS. 


i 


81 



FOURTH METHOD 

81. Let AT) be the given right 
line, and D the point at which 
the perpendicular is to he drawn. 

Take any distance on the tape 
or chain, and place one extrem- A 
ity at D, and fasten the other 

at some point, as E, between ' ^- 

the two lines which are to form the right angle. Place a 
staff at E. Then, having stationed a person at D , remove 
that extremity of the chain and carry it round until it 
ranges on the line DA at A. Place a staff at A : then 
remove the end of the chain at A, and carry it round 
until it falls on the line AE at F. Then place a staff at 
F ; ADF will be a right angle, being an angle in a 
semicircle. 


32. There is a very simple instrument, used exclusively 
in laying off' right angles on the ground, which is called 

the 


SURVEYING- CROSS. 

PI. 2, Fig. 1. This instrument consists of two bars, AB 
and CD, permanently fixed at right angles to each other, 
and firmly attached at E to a pointed staff, which serves 
as a support. Four sights are screwed firmly to the bars, 
by means of the screws a , b , c, and cl. 

As the only use of this instrument is to lay off right 
angles, it is of the first importance that the lines of sight 
be truly at right angles. To ascertain if they are so, let 
the bar AB be turned until its sights mark some distinct 
object; then look through the other sights, and place a 
staff on the line which they indicate: let the cross be then 
turned until the sights of the bar AB come to the same 
line: if the other sights are directed to the first object, the 
lines of sight are exactly at right angles. 

The sights being at right angles, if one of them be 
turned in the direction of a given line, the other will mark 
the direction of a line perpendicular to it. at the point 
where the instrument is placed. 

6 





ELEMENTS OF SURVEYING. [BOOK II 


V* 


S2 


II. From q, without a straight line, to let fall a 

/ perpendicular on the line. 

33. Let C be the given point, and AB the given line. 

From C measure £ line, as 
OA, to any point of th| line A B. 

From A, measure on AB any 
distance as AF t and at F erect 
FF perpendicular to A B. 

Having stationed a person at A , measure along tlie per 
pendicular FF until the forward staff is aligned on the line 
AC: then measure the distance AF. Now, by similar tri¬ 
angles, we have, 

AF : AF : : AC : AD, 



. \B 


in which all the terms are known except AD, which may, 
therefore, be found. The distance AD being laid off from 
A, the point D, at which the perpendicular CD meets AB, 
becomes known. If we wish the length of the perpen¬ 
dicular, we use the proportion, 

AF : FF : : AC : CD, 

in which all the terms are known, excepting CD : there¬ 
fore, CD may be determined. 


HL To determine the horizontal distance from a given point to 

an inaccessible object. 

FIRST METHOD. 

» 

34. Let A be an inaccessible object, and F the point 
from which the distance is to be measured. 

At E lay off the right angle 
AED, and measure in the di¬ 
rection ED, any convenient dis¬ 
tance to D, and place a staff 
at D. Then measure from E, 
directly towards the object A, 
a distance FB of a convenient jj 
length, and at B lay off a line B 


F 


A 


B 


K 


BC perpendicular to FA. Measure along the line BC 












SEC. I] 


PRACTICAL PROBLEMS. 


83 


until a person at D shall range the forward staff on the 
line DA. How, BF is known, being equal to the differ¬ 
ence between the two measured lines BE and GB. Hence, 
by similar triangles, 

BF : FG : : BE : JSA, 

m which proportion all the terms are known, except th 
fourth, which may, therefore, be found. 

SECOND M 

85. At the point E lay off 
EB perpendicular to the line 
EA, and measure along it any 
convenient distance, as EB. 

At B lay off the right an¬ 
gle EBB , and measure any dis¬ 
tance in the direction BD. Let 
a person at D align a staff on 
DA, while a second person at B aligns it on BE\ the 
staff will thus be fixed at 0. Then measure the dis¬ 
tance BC. 

The two triangles BCD and CAE being similar, we 
have, 

BG : BD : : CE : EA, 

m which all the terms are known, except the fourth, which 
may, therefore, be found. 

THIRD METHOD. 

86. Let B be the given point, and A the inaccessible 
object; it is required to find BA. 

Measure any horizontal base 
line, as BC. Then, having 
placed staves at B and G, 
measure any convenient dis¬ 
tances BD and CE , such that 
the points D , B, and A, shall 
be in the same right line, as 
also, the points E , C, and A ; 
then measure the diagonal lines 
DC and EB. 
















84 


EL EM ENTS OF SURVEYING. [BOOK II 


Now, in the triangle BEC [ 

tlie three sides are known, 

\ 

therefore, the angle ECB can 
be found. In the triangle CDB, 
the three sides are also known, 
therefore the angle CBB can be 
determined. These angles be¬ 
ing respectively subtracted from 
180°, the two angles ACB and 
ABO become known; and hence, 
in triangle ABO, we have two 
side, to find the side BA. 



angles and the included 


IY. To find the altitude of an object, when the distance to the 

vertical line passing through the top of it is known. 

% 

37. Let CD be the altitude required, and AC the known 
distance. 

From A, measure on 
the line AC, any con¬ 
venient distance AB, and 

place a staff vertically 'fp/ 


I , ,i • » ii 




, 


at B. Then placing the 
eye at A j sight to the 
object D, and let the 
point, at which the line AD cuts the staff BE, be marked. 
Measure the distance BE on the staff; then, 


B 


C 


AB : BE : 

whence CD becomes known. 


AC 


CD, 


If the line AC cannot be measured, on account of in¬ 
tervening objects, it may be determined by calculation, ns 
in the last problem, ind then, having found the horizontal 
distance, the vertical line is readily determined, as before. 





















SEC. II.] 


AREA OF LAND. 


85 



SECTION II. 

AREA OR CONTENTS OF GROUND.—LAYING OUT LAND. 

1. We come next to the determination of the area or 
superficial contents of ground. 

The surface of the ground being, in general, broken 
and uneven, it is impossible, without great trouble and ex¬ 
pense, to ascertain its exact area or contents. To avoid 
this inconvenience, it has been agreed to refer every sur¬ 
face to a horizontal plane: that is, to regard all its bound¬ 
ing lines as horizontal, and its area as measured by that 
portion of the' horizontal plane which the boundary lines 
enclose. 

For example, if ABCD were a 
piece of ground having an uneven 
surface, we should refer the whole 
to a horizontal plane, and take 
for the measure of the area that 
part of the plane which is inclu¬ 
ded between the bounding hori¬ 
zontal lines AB, BC] CD , DA. 

In estimating land in this manner, the sum of the areas 
of all the parts into which a tract may be divided, in equal 
to the area, estimating it as an entire piece : but thif(k r ould 
not be the case if the areas of the parts had reference to 
the actual surface, and the area of the whole were ealeu 
lated from its bounding lines. 

2. The unit of measure of a quantity is a quantity ot 
the same kind regarded as a standard, and with which all 
quantities of that kind may be compared. For lines, the 
unit is a right line of a known length, as 1 foot, 1 link, 1 
chain, or any other fixed distance. 

It has been already observed (Bk. II., Sec. I., Art. 16), 
that Gunter’s chain of four rods or 66 feet in length, and 
which is divided into 100 links, is the chain in general 






I 


86 ELEMENTS OF SURVEYING. [BOOK II 


use among surveyors. In measuring land, tlie length of 
this chain is generally taken for the unit of linear measure. 


8. The unit of measure for surfaces is a square de 
scribed on the unit of linear measure. 


1 foot. 


Thus, 1 square foot, 


1 square yard or 9 square feet, 


1 yard = 3 feet. 




1 

1 








1 square chain, or 16 square rods. 


1 chain—4 rods. 



! 
















When, therefore, the linear measures of ground are feet, 
yards, rods, or chains, the superficial measures are square 
feet, square yards, square rods, or square chains; and the 
numerical expression for the area is the number of times 
which the unit of superficial measure is contained in the 
land measured. 


4. An acre is a surface equivalent in extent to 10 square 
chains; that is. equivalent to a rectangle of which one side 
is ten chains ana the other side one chain. 

One quarter of an acre is called a rood. 

Since the chain is 4 rods in length, 1 square chain con¬ 
tains 16 square rods; and therefore, an acre, which is 10 
square chains, contains 160 square rods, and a rood con¬ 
tains 40 square rods. The square rods are called perches. 

5. Land is generally computed in acres, roods, and 
perches, which are respectively designated by the letters 
A. It P. 






















S E C. I I.J 


AREA OF LAND. 


87 




When the linear dimensions of a survey are chains or 
links, the area will be expressed in square chains or square 
links, and it is necessary to form a rule for reducing this 
area to acres, roods, and perches. For this purpose, let us 
form the following 


TABLE. 


Miles. 

Acres. 

Roods. 

Sq. Chains. 

Perches. 

Sq. Links. 

1 

640 

2560 

6400.0 

102,400 

64,000.000 


1 

4 

10.0 

160 

100,000 



1 

2.5 

40 

25,000 




1.0 

16 

10,000 





1 

625 


1 square mile = 6400 square chains = 640 acres. 


Now, when the linear dimensions are links, the area 
will be expressed in square links, and may be reduced to 
acres by dividing by 100000, the number of square links 
in an acre: that is, by pointing off five decimal places 
from the right hand. 

4 

If the decimal part, be then multiplied by 4, and five 
places of decimals pointed off from the right hand, the 
figures to the left will express the roods. 

If the decimal part of this result be now multiplied by 
40, and five places for decimals pointed off, as before, the* 
figures to the left will express the perches. 

If one of the dimensions be in links, and the other in 
chains, the chains may be reduced to links by annexing 
two ciphers : or, the multiplication may be made without 
annexing the ciphers, and the product reduced to acres- and 
decimals of an acre, by pointing off three decimal -places 
from the right hand. 

When both the dimensions are in chains, .the product • 
is reduced to acres by dividing by 10, .or pointing off one 
decimal place. 

Front which we conclude; that, 

1st. If links be multiplied by links , the product is reduced to 
aa'&s by pointing ofi five decimal places from the right"hand. 


m) • 




















ELEMENTS OF SUR7EYING. 


[COOK II. 


88 


2d. If chains he multiplied hy links , the product is reduced 
io acres hy pointing off three decimal places from the right hand. 

3d. If chains he multiplied hy chains, the product is reduced 
to acres hy piointing off one decimal place from the right hand. 

6. Since tliere are 16.5 feet in a rod, a square rod is 
equal to . 16.5x 16.5 = 272.25 square feet. 

If tire last number be multiplied by 160, we shall have, 

272.25 X 160 = 43560 = the square feet in an acre. 

Since there are 9 square feet in a square yard, if the 
last number be divided by 9, we obtain, 

4840 = the number of square yards in an acre. 


PROBLEM I. 

7. To find the area of a piece of ground in the form 
of a square, rectangle, or parallelogram. 

Multiply the base hy the altitude , and the product will express 
the area (Geom., Bk. IV., Prop. IV. and V.) 

1. To find the area of the rectangular d q 

field ABCD. 

Measure the two sides AB, BG : let us 
suppose that we have found AB — 14 chains 
27 links, and BC— 9 chains 75 links. Then, A B 

AB= 1427 links, 

BC •= 975 links, 

ABy.BC— 1391325 square links, 

= 13.91325 acres. 

% • 

4 

3.65300 roods, 

40 

4 _ 

26.12000 perches. 

Ans. 13 A. SB. 2 6P 

0 

2. What is the area of a square field, of which the 
sides are each 33 cli. 8 1. ? 

, Ans. 109 A. IB. 29P. 







SEC. II.] 


AREA OF LAND. 


89 


3. TV hat are the contents of a rectangular field, of which 
the longer side is 49 eh. 27 L, and the shorter 38 ch. 7 1. ? 

- Arts. 187A 2 R IIP. 

4* What are the contents of a field in the form of a 
parallelogram, of which the base is 35 ch. 65 1., and alti- 
tude 51 ch. 4 1.? 

Ans. 181-4. 3P. 33P. 


PROBLEM II. 

8. To find the contents of a piece of land in the form 
of a triangle. 


FIRST METHOD. 

Measure either side of the triangle 
as BC , and from the opposite angle 
A let fall a perpendicular AD, and 
measure this perpendicular / then , mul¬ 
tiply the base and perpendicular to¬ 
gether, and divide the product by 2, 
the result will express the area of the triangle. Or, the area 
is equal to the base multiplied by half the perpendicular , or to 
the perpendicular multiplied by half the base (Geom., Bk. IV., 
Prop. VI.). 

1. What are the contents of a triangle whose base is 
25 ch. 1 1., and perpendicular 18 ch. 14 1. ? 

Ans. 22A. 2R. 29P. 

2. What are the contents of a triangle whose base is 
15.48 chains, and altitude 9.67 chains ? 

Ans. 7 A. IP. 38P. 


A 



SECOND METHOD. 

Measure two sides and their included angle. Then , add 
together the logarithms of the two sides and the logarithmic sine 
of their included angle; from this sum subtract the logarithm 
of the radius , which is 10, and the remainder will be the loga¬ 
rithm of double the area of the triangle. Find , from the table } 




90 


ELEMENTS OF SURVEYING. 


[BOOK II 


the number answering to this logarithm , and divide it by 2 ; the 
quotient will be the required area (Geoin. Mens., Art. 6). 


1. In a triangle ABC, suppose that we have found 
AB — 57.65 eh., AC— 125.81 eh., and the included angle 
CAB =5 7° 25': required the area. 

Let the required area be designated by Q ; then, 

" -flog AB 57.65 . . . 1.760799 

1 „ 20= \ + lo 8 AC 125.81 . . 2.099715 

° ’ *4* log sin A 57° 25' . 9.925626 

— log R .10 

2 Q = 6111.4 .... 3.786140. 

And Q =3055.7 square chains. 

Ans. 305M. 2 R. 11 P. 


.Remark. In this example, the links are treated as de¬ 
cimal parts of the chain; the result, therefore, is in square 
chains and decimal parts of a square chain. ’ 

2. What is the area of a triangle whose sides are 80 
and 40 chains, and their included angle 28° 57' ? 

Ans. 29A. OR. 7 P. 


THIRD METHOD. 

Measure the three sides' of the triangle. Then, add them 
together and take half their sum. From this half sum subtract 
each side separately. Then , multiply the half sum and the 
three remainders together , and extract the square root of the pro¬ 
duct: the result will be the area (Geom. Mens., Art. 7). 

Or, after having obtained the three remainders , add together 
the logarithm of the half sum and■ the logarithms of the re¬ 
spective remainders, and divide their sum by 2; the quotient 
will be the logarithm of the area. * 

1. Find the area of a triangular piece of ground whose 
sides are 20, 30, and 40 chains. 

/ 






S E 0. I1] 


AREA OF LAND. 


91 


BY FIRST RULE. 

20 45 45 45 

30 -20 - 30 - 40 

40 25 1st rem. 15 2d rem. 5 3d rem. 

2)90 — — _ 

45 — half sum. Then, 

45 X 25 X 15 X 5 = 84375 : and ^84375 = 290.4737 = the 
area. 

Ans. 29A. OR. SP. 

2. What is the area of a triangle whose sides are 2569, 
4900, and 5035 links? 


BY SECOND RULE. 

2569 6252 6252 6252 

4900 -2569 -4900 -5035 

5035 3683 1st rem. 1352 2d rem. 1217 3d rem. 


2)12504 


6252 = half sum. 


Then, 


f log 6252 
lose 3683 


J 


log 1352 
log 1217 


Area in square knks, 6155225 . 


. 3.796019 
. 3.566202 
. 3.130977 
. 3.085291 
2)l3A78489 
. 6.789244. 


Ans. 61 A. 2 R. 8P. 


PROBLEM III. 

9. To lina the area of a piece of land in the form oh 
a trapezoid. 

Measure the two parallel sides , and also the perpendicular 
distance between them. Add the two parallel sides together , 
and take half the sum,; then multiply the half sum by the 
perpendicular, and the product will be the area. (Greom., Bk. 
IV., Prop. VII.) 





















92 


ELEMENTS OF SURVEYING. [BOOK 11 


1. What is the area of a trapezoid, 
of which the parallel sides are SO and 
49 chains, and the perpendicular distance 
between them 16 ch. 60 1., or 16.60 chains ? 

80 + 49 = 79; dividing by 2, gives . . 89.5 
multiply by.16.60 

area in square chains. 655.700. 

Am. 65+. 2 R. 11 P. 



2. Required the contents, when the parallel sides are 20 
and 82 ch., and the perpendicular distance between them 
26 ch. 

Am. 67 A. 2 B. 16P 


PROBLEM IV. 

10. To find the area of a piece of land in the form of 
a quadrilateral. 

Measure the four sides of the quadrilateral , and also one of 
the diagonals: the quadrilateral will thus he divided into two 
triangles, in both of which all the sides will he known. Then, 
find the areas of the triangles separately, and their sum will he 
the area of the quadrilateral. 

1. Suppose that we have measured 
the sides and diagonal AO, of the 
quadrilateral ABCB, and found 
AB = 40.05 ch. CD = 29.87 ch., 

BC = 26.27 ch. AD = 87.07 cli., 
and +67=55 ch.: 

required the area of the quadrilateral. 

Am. 101+. IB. 15 R 

Remark. Instead of measuring the four sides of the 
quadrilateral, we may let fall the perpendiculars Bb, Bg , on 
the diagonal AC. The area of the triangle may then bo 
determined by measuring these perpendiculars and the di¬ 
agonal AC. The perpendiculars are Bg — 18.95 ch , an of 
Eh= 17.92 eh. 


I) 















dEC. II.] 


AREA OF LANE. 


93 


PROBLEM V. 

11. To find the contents of a field having any number 
of sides. 


Measure the sides of the field and also the diagonals: the 
three sides of each of the triangles into which the field will he 
thus divided will then he known , and the areas of the triangles 
may then he calculated by the preceding rules. Or, measure 
'he diagonals , and from the angular points of the field draw 
perpendiculars to the diagonals and measure their lengths: the 
base and perpendicular of each of the triangles will then he 
known. 


1. Let it be required to determine the contents of the 
field ABODE\ having five sides. 

Let us suppose that we have mea¬ 
sured the diagonals and perpendicu¬ 
lars, and found, 

AC= 36.21 ch., EC— 39.11 eh., 

Bh = EQ8 ch., Dd= 7.26 ch., 

Aa = 4.19 ch. ; required the area of the field. 



Area of triangle ABC— 73.8684 square chains, 

area of “ CDE= 141.9693 “ 

area of “ ACE— 81.7399 “ “ 

area of ABODE— 297.5776 “ “ 

Ans. 29 A. 3A IP. 


PROBLEM VI. 

12. To find the contents of a long and irregular figure, 

O 0 0 7 

bounded on one side by a straight line. 

Suppose the ground, of which the contents are required, 
to be of the form ABEeda , bounded on one side by the 
right line AE, and on the other by the curve edca. 

At A and P, the extremities of 
the right line AE. erect the two per¬ 
pendiculars Pe, and on each of 
them measure the 1 readth of the land. 















94 


ELEMENTS OF SURVEYING. [BOOKIL 




Then divide the base into any convenient number of equal 
parts, and measure the breadth of the land at each point 
of division. 

Add together the intermediate breadths and half the sum of 
the two extreme ones: then multiply this sum by one of the 
equal quarts of the base line , and the product will be the re¬ 
quired area very nearly (Mens. Art. 11). 

1. The breadths of an irregular figure, at five equidis¬ 
tant places, being 8.20 ch., 7.40 ch., 9.20 ch., 10.20 ch., and 
8.60 chains, and the whole length 40 chains, required the 
area. 

• 8.20 4)40 

8.60 10 one of the equal parts. 

2 )16.80 “ 

8.40 mean of the extremes, 85.20 sum, 

7.40 _10 

9.20 area 852.00 square ch. 

1 0.20 . ' 

85.20 sum. 

A ns. 85 A. 32 P. 

2. The length of an irregular piece of land being 21 ch., 
and the breadths, at six equidistant points, being 4.35 ch., 
5.15 ch., 8.55 ch., 4.12 cli., 5.02 ch., and 6.10 chains: re¬ 
quired the area. 

Ans. 9 A. 2 R. 30 P. 

» 

3. The length of an irregular piece of land is 80 ch., 
and the breadths at nine equidistant points are 5.75 ch., 
6.12 ch., 4.80 cli., 5.09 ch., 8.87 ch., 5.17 ch., 6.00 ch., 
3.94 ch., and 5.95 ch.: what is the area? 

Ans. 40A. SR. 14P. 

4. The length of an irregular field is 39 rods, and its 

breadths at five equidistant places are 4.8, 5.2, 4.1, 7.3, and 
7.2 rods: what is its area? Ans. 220.35 sq. rods. 

Remark. If it is not convenient to erect the perpen¬ 
diculars at equal distances from each other, the areas of 
the trapezoids, into which the whole figure is divided, 
must be computed separately : their sum will be the re¬ 
quired area. 








SEC. II.] 


AREA OF LAND. 


95 


PROBLEM VII. 

13. To find the area of a piece of ground in the form 
of a circle. 


Measure the radius AC: then multiply 
the square of the radius by 3.1416 (Mens., 
Art. 15.). 



1. To find the area of a circular piece of land, of which 
the diameter is 25 ch. 


Ans. 49A. OR. 14 P. 


PROBLEM VIII. 


14. To find the contents of a piece of ground in the 
form of an ellipse. 


Measure the semi-axes AE\ CE. Then 
multiply them together , and their product 

by 3.1416. 



1. To find the area of an elliptical piece of ground, of 
which the transverse axis is 16.08 ch., and the conjugate 
axis 9.72 ch. 

Ans. 12 A. 1 R. 4P. 


Remark I. The following is the manner of tracing an 
ellipse on the ground, when the two axes are known. 

From C ) one of the extremities of the conjugate axis 
as a centre, and AE half the transverse axis as a radius, 
describe the arc of a circle cutting AE in the two points 
F and G : these points are called the foci of the ellipse. 

Then, take a tape, the length of which is equal to AB, 
and fasten the two ends, one at the focus F : the other at 
the focus G. Place a pin against the tape and move it 
around, keeping the tape tightly stretched: the extremity 
of the pin will trace the curve of the ellipse. 

Remark II. In determining the contents of ground, in 
the examples which have been given, the linear dimensions 
have been taken in chains and decimals of a chain. 







96 ELEMENTS OF SURVEYING [BOOK II 

If the linear dimensions were taken in terms of any 
other unit, they may he readily reduced to chains. For, 
a chain is equal to 4 rods, equal to 22 yards, equal to 66 
feet. lienee, 

1st. Rods may be reduced to chains and the decimal of a 
chain , by dividing by 4. 

2d. Yards may be reduced to chains and the decim,al of a 
chain , by dividing by 22. 

3d. Feet may be reduced to chains and the decimal of a 
chain r by dividing by 66. 

Remark III. If it is thought best to calculate the area, 
without reducing the linear dimensions to chains, the re¬ 
sult can be reduced to acres: 

1st. By dividing it by 160 ivlien it is in square rods 
(Art. 5). 

2d. By dividing it by 4840 when it is in square yards 
(Art. 6). 

3d. By dividing it by 43560 when it is in square feet 
(Art. 6). 


OF LAYING OUT LAND. 

15. The survej^or is often required to lay off a given 
quantity of land, in such a way that its bounding lines 
shall form a particular figure, viz., a square, a rectangle, a 
triangle, &c. He is also often called upon to divide given 
pieces of land into parts containing given areas, or bearing 
certain relations to each other. 

The manner of making such divisions must always de¬ 
pend on a judicious application of the principles of geom¬ 
etry to the particular case. 

If, for example, it were required to lay out an a^re of 
ground in a square form, it would first be necessary to 
find, by calculation, the side of such a square, and then to 
trace, on the ground, a figure bounded by four equal line? 
at right angles to each other. 


SEC. Ill 


LAYING OUT LAND. 


97 


PROBLEM I. 

16. To lay out a given quantity of land in a square 
form. • 

Reduce the given area to square chains , or square rods: 
then extract the square root , and the result will he the side of 
the required square. This square being described on the ground , 
will be the figure required. 

1. To trace a square which sliall contain 15A. OR. 12 P. 

First, 15A = 60 R — 2400 P 

Add, 12P; hence, 

15.4 OR 12P=2412P; the square root 

of which is 49.11. 

Therefore, if a square be traced on the ground, of which 
the side is 49.11 rods, it will be the required figure. 

2. To trace a square which shall contain 176.4. IP. 24P 

First, 176A = 1760 square chains, 

1 R= 2.5 “ 

hence, 24P = 1.5 “ “ 

176A 1 R 24P=1764 square chains: the square 
root of which is 42. Hence, if a square be traced on the 
ground, of which the side is 42 ch., it will be the required 
figure. 

O 


PROBLEM II. 


17. To lay out a given quantity of land in a rectangu¬ 
lar form, having one of the sides of the rectangle given. 


Divide the given area, reduced to square chains or square 
reds , by the given side of the required rectangle , and the quotient 
will be the other side. Then , trace the rectangle on the ground . 

1. To lay off 240 acres in a rectangular form, one of 
the sides being given, and equal to 80 rods. 

First, 240A = 2400 square chains = 38400 square rods.. 

Then, 80)38400(480 rods; which is the required side: 
of the rectangle. 


18. A great, number of similar problems might be pro¬ 
posed. The solution of them does not, however, properly 
belong to surveying. The laying out of the ground, and 

7 





9 8 ELEMENTS OF SURVEYING. [BOOK II 

the tracing of lines, after the figure and area have been 
determined, are the only parts which appertain to a prac¬ 
tical treatise. The manner of tracing lines having been al¬ 
ready explained, it seems unnecessary to add the numerous 
examples often given under this head of the subject. 


SECTION III. 

* 

SURVEYING WITH THE COMPASS.—DIVIDING LAND. 

1. Before considering the principles involved in the 
method of surveying now to be explained, it will be ne¬ 
cessary to describe the instrument principally used in the 
field, and which is called 

THE CIRCUMFERENTER, OR SURVEYOR’S COMPASS. 

PI. 2, Fig. 2. This instrument consists of a compass-box 
BCE , a magnetic needle, a brass plate AB, from twelve to 
fourteen inches long, two plain sights, AF and BG, one 
of which is more fully shown in Fig. 3; and a stand, 
which is sometimes a tripod, and sometimes a single staff 
pointed with iron at the lower end, so that it may be 
placed firmly in the ground. 

The open sights, AF and BQ, are placed at right an¬ 
gles to the plate AB, and fastened to it firmly by the 
screws a and b. In each sight there is a large and small 
aperture or slit; the larger aperture being above the smaller 
in one of the sights, and below it in the other. A hair 
or thread of silk is drawn vertically through the middle 
of the large aperture, as shown in Fig. 3. 

The compass-box BCE is circular, and generally about 
eix inches in diameter. At the centre is a small pin, on 
which the magnetic needle is poised. This needle, if al- 
lowerl to turn freely around the point of support, will settle 
to a state of rest: the direction which it then indicates, is 
that of the macinetic meridian . 



SEC. HI.] 


WITH THE COMPASS. 


99 


In the interior of the compass-box, there is a graduated 
circle divided to degrees, and sometimes to half degrees . 
the degrees are numbered from the extremities of the di¬ 
ameter NS, both ways to 90°. 

The length of the magnetic needle is a little less than 
the diameter of the graduated circle, so that the needle can 
move freelv around its centre, within the circle, and its 

7 7 

positions be noted on the graduated arc. 

The compass-box is turned about its centre, without 
moving the plate AB , by means of the milled screw L : 
it is fastened to the plate AB, by the screw P. 

In using the compass, it is important to ascertain the 
exact angle which may be included between the magnetic 
meridian and the direction that may be given to the line 
drawn through the eye and the sights AF and BG. 

To effect this, a small arc HI is described on the bar 
AB , having its centre at the centre of the compass-box. 
This arc is divided to degrees, and sometimes to the parts 
of a degree. A vernier is also used, which is permanently 
attached to the compass-box. 

When the 0 point of this vernier coincides with the 0 
point of the graduated arc III, the line of the compass-box 
marked NS, lies in the plane of the sights. 

Now, supposing the 0 of the vernier to coincide with 
the 0 of the arc III, if the end of the needle does not 
stand at one of the lines of division of the graduated 
circle, let the whole degrees be read. Then, turn the 
compass-box by means of the screw L, until the needle 
points exactly to the line which marked the whole degrees: 
the space passed over by the 0 of the vernier, shows the 
parts of a degree that are to be added to give the true 
reading. 


SURVEYING- WITH THE COMPASS. 

2. The line about which the earth revolves is called its 
axis; and the two points in which the axis meets the sur¬ 
face of the earth, are called the poles. 

3. A plane passed through the axis is called a meridian 

wore. 


ELEMENTS OF SURVEYING. 


100 


[BOOK II 


plane, and its intersection with, the surface is called a me¬ 
ridian line or a meridian. 

4. All the meridians converge towards the poles, but 
they vary so little from parallelism within the narrow limits 
of surveys made with the compass, that they may, without 
error, be regarded as parallel straight lines. 

5. If a magnetic needle be suspended freely and allowed 
to settle to a state of rest, a vertical plane passed through 
its axis is called the plane of the magnetic meridian; and its 
intersection with the surface of the earth is called the mag¬ 
netic meridian, or sometimes a North and South line. A 
line perpendicular to a North and South line is called an 
East and West line. 


\ 


6. A line traced or measured on the ground, is called 


a course; and the angle which 
meridian passing through the 
point of beginning, is called 
the bearing. 

Thus, if we start from the 

point A, and measure in the 

direction AB. the line AB is 
/ 

the course, and the angle A AB 
is the bearing. 


this line makes with the 

N 



When the course, like AB, falls between the north and 
east points, the bearing is read, north 46° east, and is 
written N. 46° E. 

When the course, like AC, falls between the north and 
west points, the bearing is read, north 30° west, and is 
written N. 30° W. 

When the course, like AF, falls between the south and 
east points, the bearing is read, south 70° east, and is writ¬ 
ten S. 70° E. 

When the course, like AD, falls between the south and 
west points, the bearing is read, south 70° west, and is 
written S. 70° W. 

A oourse which runs due north, or due south, is desig¬ 
nated by the letter N or S ; and one which runs due east, 
or due west, by the letter E or W. 





SEC. III.] 


WITH THE COMPASS. 


101 


7. If, after having passed over a course, the hearing is 
taken to the back station, this bearing is called the bach 
sight , or reverse bearing. 


8. The perpendicular distance between the east and west 
lines drawn through the extremities of a course, is called 
the northing or southing , according as the course is run to¬ 
wards the north or south. This distance is also called the 
difference of latitude , or simply the latitude, because it shows 
the distance which one of the points is north or south of 
the other. 




S 


Thus, in running the course from A 
to B, AC is the difference of latitude, 
north. 


tween the meridians passing through the 
extremities of a course, is called the de¬ 
parture of that course, and is east or 
west, according as the course lies on 
the east or west side of the meridian passing through the 
point of beginning. 


p 

H 

t/ 

G 

r 

i A *■ 

J 

■yF 
/ r 

A 



Thus, in running the course AB\ CB is the departure, 
east. 


10. It will be found convenient, in explaining the rules 
for surveying with the' compass, to attribute to the lati¬ 
tudes and departures the algebraic signs, + and —. 

We shall, therefore, consider every northing as affected 
with the sign -f, and every southing as affected with the 
sign —. We shall also consider every easting as affected 
with the sign +, and every westing as affected with the 
sign —. 

11. The meridian distance of a point is its perpendicular 
distance from an assumed meridian. Thus, if the distance 
be estimated from the meridian NS, BC will be the meri¬ 
dian distance of the point B. 


12. The meridian distance of a line is the meridian dis¬ 
tance of its middle point, and is east or west, according as 
this point lies on the east or west side of the assumed me- 







102 


ELEMENTS OF SURVEYING. [BOOK II 


ridian. Thus, FG drawn through the middle point of AB t 
is the meridian distance of the line AB. 

The sign -f will always be given to the meridian dis¬ 
tance of a point or line, when it lies on the east of the as¬ 
sumed meridian, and the sign —, when it lies on the west. 

i 

13. When a piece of ground is to be surveyed, we be¬ 
gin at some prominent corner of the field, and go entirely 
around the land, measuring the lengths of the bounding 
lines with the chain, and taking their bearings with the 
compass. It is not material whether the ground be kept 
on the right hand or on the left, and all the rules deduced 
for one of the cases, are equally applicable to the other. 
To preserve uniformity, however, in the language of the 
rules, we shall suppose the land to be always kept on the 
right hand of the surveyor. 


FIELD OPERATIONS. 


14. Let A BCD be a piece of 
ground to be surveyed, A the point 
where the work is to be begun, 
and NS a meridian. 

On a sheet of paper, rule three 
columns, as follows, and head them 
stations, bearings, distances. 


N 



Stations. 

Bearings. 

Distances. 

1 

2 

3 

' 4 

N 31i° W 

N 62|° E 

S 36° E 

S 451° W 

10. 

9.25 

7.60 

10.40 


Place the compass at A, and take the bearing to B ; 
which is BAB: suppose this angle has been found to be 
The bearing from A to B is then N. 31£° W. En- 


31 Y 













S Ifi C. 111. j 


WITH THE COM TASS. 


103 


ter this bearing in the held notes opposite station 1. 
Then measure the distance from A to _Z>, which we will 
suppose to be 10 ch., and insert that distance opposite star 
tion 1, in the column of distances. 

We next take the bearing from B to (7, 1ST. 62J E., and 
then measure the distance BC—9 ch. 25 L, both of which 
we insert in the notes opposite station 2. 

At station C we take the bearing to l), S. 36° E., and 
then measure the distance CD-—1 ch. 60 1., and place them 
in the notes opposite station 3. 

At D we take the bearing to A, S. 45J° W., and mea¬ 
sure the distance DA = 10 ch. 40 1. We shall then have 
made all the measurements on the field which are neces¬ 
sary to determine the contents of the ground. 

15. Remark I. The reverse bearing or back sight, from 
B to A, is the angle ABH ; and since the meridians NS 
and JIG are parallel, this angle is ecjual to the bearing 
NAB. The reverse bearing is, therefore, S. 31-|° E. 

The reverse bearing from C\ is S. 62f° W.; that is, it 
is the angle ICB— GBC. 

And generally, a reverse bearing , or bach sight, is always 
'equal to the forward bearing , and differs from it in both of the 
letters by which it is designated. 

16. Remark II. In taking the bearings with the com¬ 
pass, there are two sources of error. 1st. The inaccuracy 
of the observations: 2d. Local attractions, or the derange¬ 
ment which the needle experiences when brought into the 
vicinity of iron-ore beds, or any ferruginous substances. 

To guard against these sources of error, the reverse 
bearing should be taken at every station: if this and v the 
forward bearing are of the same value, the work is proba¬ 
bly right; but if they differ considerably, they should both 
be taken again. 

17. Remark III. If the forward and back sights at the 
end of any course of the survey agree, it may be safely 
assumed, that no local attraction disturbs the needle at 
these points; and hence, that the next foresight is also free 
from such disturbing causes. The error, therefore, from 


104 


ELEMENTS OF SURVEYING. [BOOK IL 


local attraction, when it arises, will first show itself in the 
difference between a true foresight and an erroneous back 
sight. 

When this difference appears, subtract the back sight 
from the foresight, and call the difference the correction for 
the next foresight. The correction will be positive when 
the foresight is the larger, and negative when it is less. 

Add this correction, with its proper sign, to the fore¬ 
sight of the next course, when the meridional and longitu¬ 
dinal letters of that course are both the same, or both dif¬ 
ferent from the foresight of the previous course, and sub¬ 
tract it when one of the letters is the same and the other 
different: the result will be the true bearing. The true 
bearing of any other course may be found by the same 
process. 


EXAMPLE. 


True Foresights. 

Back Sights. 

Foresights of next 
Course. 

Foresights 

Corrected. 

1. S 85° 10' W 

2. N 16° 20' E 
8. N 17° 25' W 
4. S. 47° 18' E 

N 85° 05' E 
S 18° 20' W 
S 16° 10' E 
N48°10'W 

S 16° 15' W 
N15° 25' W 
N 28° 16' E 
S 49° 15' W 

S 16° 20' W 
N17° 25'W 
N 27° 01' E 
N 50° 07' W 


Note.— If there be no course in the survey in which 
the fore ward and back sights agree, take the one in which 
they agree the nearest, and add half the difference of the 
bearings to the least, and treat the result as the true bearing 

O* 

18. Remark I\ r . In passing 
over the course AB , the north¬ 
ing is found to be //A, and the 
departure, which is west, is repre¬ 
sented by AIL Of the course BC\ 
the northing is expressed by BG, 
and the departure, which is east, 
by GO. Of the course CD, the 
southing is expressed by CL , and 
the departure, which is east, by 
CF. Of the course DA, the south- 


TST 















SEC. Ill] 


TRAVERSE TABLE. 


105 


ing is expressed by KA, and the departure, which is west, 
by DK. It is seen from the figure, that the sum of 
the northings is equal to HB + BG — HGr ; and that the 
sum of the southings is equal to ClAKA=PA — HG: 
hence, the sum of the northings is equal to the sum of the 
southings. 

If we consider the departures, it is apparent that the 
sum of the eastings is equal to GCA- CF— GF\ and that 
the sum of the westings is equal to AHADK— GF\ hence 
also, the sum of the eastings is equal to the sum of the westings. 
We therefore conclude, that when any survey is correctly 
made, the sum of the northings will be equal to the sum of the 
southings , and the sum of the eastings to the sum of the 
westings. 

It would indeed appear plain, even without a rigorous 
demonstration, that after having gone entirely round a 
piece of land, the distance passed over in the direction due 
north, must be equal to that passed over in the direction 
due south ; and the distance passed over in the direction 
due east, equal to that passed over in the direction due 
west. 

Having now explained the necessary operations on the 
field, we shall proceed to show the manner of computing 
the contents of the ground. We shall first explain, 


THE TRAVERSE TABLE AND ITS USES. 

19. This table shows the latitude and departure corres¬ 
ponding to bearings that are expressed in degrees and 
quarters of a degree from 0 to 90°, and for every course 
from 1 to 100, computed to two places of decimals. 

The following is the method of deducing the formulas 

O O 

for computing a traverse table; by means of these for¬ 
mulas and a table of natural sines, the latitude and depar¬ 
ture of a course may be computed to any desirable degree 
of accuracy. 


106 


ELEMENTS OF SURVEYING. [BOOK II 


Let AD represent any course, and 
NAD — A CB , expressed in degrees and 
minutes, be its bearing. Let AC be the 
unit of measure of the course, and also 
the radius of tbe table of natural sines 
(Bk L, Sec. III., Art. 14). Draw DE and 
CB parallel to NS, and AE perpen¬ 
dicular to AS. Then will DE be the 
latitude , and AE the departure of the course , and CB the co¬ 
sine, and AB the sine of the hearing. 

From similar triangles we have these proportions, 

AC : CB : : AD : DE, or 

1 : cos of the bearing : : course : latitude, 

AC : AB : : AD : AE, or 

1 : sin of the bearing : : course : departure. 

Whence, lat. = course X cos of the bearing, 
dep. = course X sin of the bearing. 

We have then the following practical rule for compu¬ 
ting the latitude and departure of any course. 

Look in a table of natural sines for the cosine and sine of 
the hearing. Multiply each by the length of the course, and the 
first product will he the latitude, and the second will he the 
departure of the given course. 



EXAMPLES. 

1. The bearing is 65° 39', the course 69.41 chains : what 


is the latitude, and what the departure? 

Natural cosine of 65° 39'.41231 

Length of the course.69.41 

Product, which is the Dif. of Latitude, 28.6184371. 

Natural sine of 65° 39'.91104 

Length of the course.69.41 

Product, which is the Departure . . 63.2352864. 













SEC. III.] 


TRAVERSE TABLE. 


10? 


2. The bearing is 75° 47', the coarse 89.75 chains : what 


is the latitude, and what the departure? 

Natural cosine of 75° 47'.24559 

Length of course. . 89.75 

Product, which is the Dif. of Latitude, 22.0417025. 

Natural sine of 75° 47'.96937 

Length of course.89.75 

Product, which is the Departure . . 87.0009575. 


IN 

c 


a 


W- 


A 


H / 

T7\B 


'A 
-—/F 


E 


20. In this manner the traverse table given at the end 
of the book has been computed. When the bearing is 
given in degrees and quarters of a degree, and the differ¬ 
ence of latitude and departure are required to only two 
places of decimals, they may be taken directly from the 
traverse table. 

If the bearing is less than 45°, the angle will be found 
at the top of the page ; if greater, at the bottom. Then, 
if the distance is less than 50, it will be found in the col¬ 
umn “distance,” on the left hand page; if greater than 50, 
in the corresponding column of the right hand page. 

The latitudes or departures of courses 
of different lengths, but which have the 
same bearing, are proportional to the 
lengths of the courses. Thus, in the 
figure, the latitudes AG, AG , or the de¬ 
partures GF ) OB, are to each other as 
the courses AF, AB. 

Therefore, when the distance is greater than 100, it 
may be divided by any number which will give an exact 
quotient, less than 100 : then the latitude and departure of 
the quotient being found and multiplied by the divisor, the 
products will be the latitude and departure of the wdiole 
course. It is also plain, that the latitude or departure of two 
or more courses, having the same bearing, is equal to the 
sum of the latitudes or departures of the courses taken sepa¬ 
rately. 

Hence, if we have any number greater than 100, as 
614, we have onlv to recollect that, 610 + 4=614; and 
also, that the latitude and departure of 610, are ten times 


S 










108 , ELEMENTS OF SURVEYING. [BOOK II 

as great, .respectively, as tlie latitude and departure of 
61: that is, equal to the latitude and departure of 61 mul¬ 
tiplied by 10, or with the decimal point removed one place 
to the right. 


EXAMPLES. 


1. To find the latitude and departure for the bearing 
29J-°, and the course 614. 


Latitude for 610 . 
Latitude for 4 . 

Latitude for 614 . 


530.90 

3.48 


Departure for 610 . 
Departure for 4 . 


534.38 


Departure for 614 . 


300.40 

1.97 

302.37 


In this example, the latitude and departure answering 
to the bearing 29^°, and to the distance 61, are first taken 
from the table, and the decimal point removed one place 
to the right: this gives the latitude and departure for the 
distance 610; the latitude and departure answering to the 
same bearing and the distance 4, are then taken from the 
table and added. 


2. To find the latitude and departure for the bearing 
62J°, and the course 7855 chains. 


Latitude for 7800 . 3602.00 Departure for 7800 . 6919.00 
Latitude for 55 . 25.40 Departure for 55 . 48.79 


Latitude for 7855 . 3627.40 


Departure for 7855 


6967.79 


Remark. When the distances are expressed in whole 
numbers and decimals, the manner of finding the latitudes 
and departures is still the same, except in pointing off the 
places for decimals: but this is not difficult, when it is re¬ 
membered that the column of distances in the table, may 
be regarded as decimals, by removing the decimal point to 
the left in the other columns. 

3. To find the latitude and departure for the bearing 
47f°, and the course 37.57. 

Latitude for 37.00 . 24.88 Departure for 37.00 . 27.39 

Latitude for .57 . .38 Departure for .57 . .42 

Departure for 37.57 . 27.81 


Latitude for 37.57 . 25.26 























8 E C. 111] 


OF BALANCING. 


109 


OF BALANCING THE WORK. 

2i. The use of the traverse table being explained, we 
can proceed to compute the area of the ground. 

The field notes having been completed, rule a new table, 
os below, with four additional columns, two for latitude, 
and two for departure. 

Then find, from the traverse table, the latitude and de¬ 
parture of each course, and enter them in the proper col¬ 
umns opposite the station. 

Then add up the column of northings, and also the col¬ 
umn of southings: the two Sums should be equal to each 
other. If they are not, subtract the less from the greater; 
the remainder is called the error in latitude. This error 
takes the name .of that column which is the less. For 
example, if the sum of the northings is less than the sum 
of the southings, the error is called, error in northing: but 
if the sum of the southings is less than the sum of the 
northings, the error is called, error in southing. We find 
the error for each particular course by the following pro¬ 
portion. 

As the sum of the courses 
Is to the error of latitude, 

So is each particular course 
To its correction. 

The error thus found may be entered in a separate col¬ 
umn ; after which add it to the latitude of the course when 
the error and latitude are of the same name , but subtract 
it when they are of different names. This will make the 
sum of the northings equal to the sum of the southings, 
and is called balancing the work. The northings and south 
ings, thus corrected are entered in columns on the right, 
, under the head bcdanced. 

The eastings and westings are balanced in the same 
manner; the difference between their sums 1 being called 
erroi in departure. 

For an example, we will resume the one already con¬ 
sidered 


110 


ELEMENTS OF SURVEYING. [BOOK II 



Error in Northing . 

As 

37.25 : 

0.68 : 

As 

37.25 : 

0.68 : 

As 

37.25 : 

0.68 : 

As 

37.25 : 

0.68 : 

As 

37.25 : 

0.06 

As 

37.25 : 

0.06 

As 

37.25 : 

0.06 

As 

37.25 : 

0.06 


0.G8 





LATITUDE. 

DEPARTURE. 



BALANCED. 

Sta. 

Bearings. 

Distan¬ 

ces. 

N. 

+ 

S. 

E. 

+ 

W. 

Cor. 

Let. 

Cor. 

Dep. 

N. 

+ 

S. 

E. 

+ 

W. 

1 

N 31 p w 

10. 

8.53 



5.22 

-{-0.18 

+ 0.02 

8.71 



5.24 

2 

N 62JO E 

9.25 

4.23 


8.22 


+ 0.17 

— 0.01 

4.40 


8.21 


3 

S 36° e 

7.60 


6.15 

4.47 


— 0.14 

— 0.01 


6 01 

4.46 


4 

S 45p w 

10.40 


7.29 


7.4 i 

—0.19 

+ 0.02 


7.10 


7.43 

Sum of courses, 

37.25 

12.76 

_ 

1344 

12.76 

12.69 

12.63 

12.63 

13.11 

13.11 

12.67 

12.67 


0.0G Error in Westing. 


10 : 0.18 error in lat. of 1st course 

9.25 : 0.17 error in lat. of 2d course. 
7.60 : 0.14* error in lat. of 3d course. 
10.40 : 0.19 error in lat. of 4th course. 

10 : 0.02* error in dep. of 1st course. 

9.25 : 0.01 error in dep. of 2d course. 
7.60 : 0.01 error in dep. of 3d course. 
10.40 : 0.02 error in dep. of 4th course. 


22. Remark I. In finding the error in latitude or de¬ 
parture, for a particular course, the last figure is sometimes 
doubtful: in which case it is best to mark it, as in the 
third proportion for error in latitude, and the first for er¬ 
ror in departure; and then, if the figures taken do not 
balance the work, let each be increased or diminished by 1. 


23. Remark II. It has already been observed (Art. 18), 
that if the measurements on the field be correctly made, 
the sums of the northings and southings will be equal to 
each other, as also those of the eastings and westings. It 
is the opinion of some surveyors, that when the error in 
latitude or departure exceeds one link for every five chains 
of the courses, the field notes ought not to be relied on 
This, perhaps, is a higher degree of accuracy than can be 
attained. The error, however, should always be made 
considerably less than one link to a chain. 


24. The following is an example in which the latitude 
and departure of each course have been computed from 
the table of natural sines. 



















































8 EC. 111.] 


yji< BALANCING 


111 


Sta. 

Bearings. 

Dist. 

Dif. of Latitude. 

Departu. e. 

Balanced. 

N. 

S. 

E. 

W. 

N. 

S. 

E. 

W. 

1 

O • 

N 45 55 VV 

53 ch. 

36.87210 



38.07149 

36.65908 



33.07149 

2 

N 4 50 E 

74.40 

74.13513 


6.26894 


73.72813 


6.26894 


3 

K 89 05 E 

125.50 

2.00800 


125.48368 


1.95126 


125.49228 


4 

S 1 50 W 

71.80 


71.76338 


2.296SS 


72.17110 


2.296S8 

5 

S 7 40 E 

31.20 


30.92107 

4.16239 



31.12133 

4.16239 


6 

N 89 25 W 

35.50 

0.36139 



35.49822 

0.36139 



35.49822 

1 

S 84 35 W 

40. 


3.77600 


39.82120 


3.80352 


39.81260 

8 

S 74 35 W 

21. 


5.5S261 


20.24442 


5.61385 


20.24442 


113.37662'l12.0430J 
112.04309' 

135.91501 

135.932211112.70986;112.709851135.82361 
135.91501! 1 

135.92361 


Error in Southing 1.83353 0.01720 Error in Easting. 

Half Error 0.60616 0.00860 Half Error. 


Instead of balancing by the method just explained, wo 
divide each error by two. Now if we subtract half the 
error in southing from the column of northings, and at the 
same time add it to the column of southings, these two 
columns will exactly balance. In like manner, if we sub¬ 
tract half the error in easting from the column of westings, 
and at the same time add it to the column of eastings, 
these columns will also balance. 

The errors should be distributed in proportion to the 
lengths of the courses, but this may be done with sufficient 
accuracy without making the proportions. If any of the 
courses have been run over rough ground, the probability 
is that the errors belong to these courses, and they should 
be distributed among them. 

In this example we separate the half error in southing 
into the three parts .40700, .21802, and .04674, and subtract 
them respectively from the northings of courses 2, 1, and 
3, and then place the northings in the balanced columns. 
For the southings we separate the half error into the four 
parts .40772, .20031, .03121, and .02752, and add them respec¬ 
tively to the southings of the courses 4, 5, 8, and 7. We 
then enter the southings in the balanced columns. As the 
error in easting is so small, we add half of it to the east¬ 
ing of course 3, and subtract half from the westing ol 
course 7. 










































112 


Jfi LAMENTS OF SURVEYIN’O. [BOOK II 


OF THE DOUBLE MERIDIAN DISTANCES OF THE COURSES. 

25. After the work has been balanced, the next thing 
to be done is to calculate the double meridian distance of 
each course. 

For this purpose, a meridian line is assumed, lying 
either wholly without the land, or passing through any 
point within it. It is, however, most convenient to take 
that meridian which passes through the most easterly or 
westerly station of the survey; and these two stations are 
readily determined by inspecting the held notes. 

Having chosen the meridian, let the station through 
which it passes, be called the principal station , and the 
course which begins at this point, the first course. Care, 
however, must be taken, not to confound this with the course 
which begins at station 1, and which is the first course that is 
entered in the field notes. 

It has already been remarked (Art. 10), .that all de¬ 
partures in the direction east, are considered as plus, and 
all departures in the direction west as minus. 


26. To deduce a rule for finding 
distances of the courses. Let BC 
represent any course, and AB the 
preceding course; also, let D and 
E be their middle points. Draw 
Eli, CM, and DC, perpendicular to 
the assumed meridian NS. Draw 
also A I, EE \ and BL, parallel to 
NS. Then 2 DC is the double me¬ 
ridian v distance of the course BC, 
and 2EII- 2KG, is the double me¬ 
ridian distance of the course AB. 

How, 2DG—2GK+ 2KL + 2LD ; 


the double meridian 

N 



but 2 KL — IL is the 


departure of the course AB, and 2LD = MC is the depar¬ 
ture of the course BC] 


consequently, 2 CD = 2 GK + ID -f MC ; 

hence, the double meridian distance of a course, is equal 
to the double meridian distance of the preceding course 








113 


SEC. III.] DOUBLE MERIDIAN DISTANCES 

plus tlie departure of that course plus the departure of the 
course itself; if there is no preceding course, the first 
two terms become zero. We therefore have the following 

RULE. 

I. The double meridian distance of the first course is equal 
to its departure. 

II. The double meridian distance of the second course is 
equal to the double meridian distance of the first course , plus 
its departure , plus the departure of the second course. 

III. The double meridian distance of any course is equal 
to the double meridian distance of the preceding course , plus 
its departure , plus the departure of the course itself. 

27. Remark. It should be recollected that plus is here 
used in its algebraic sense, and that when the double me¬ 
ridian distance of a course and the departure which is to 
be added to it, are of different names, that is, one east and 
the other west, they will have contrary algebraic signs; 
hence, their algebraic sum will be expressed by their dif¬ 
ference, with the sign of the greater prefixed to it. 

If the assumed meridian cuts the enclosure, the double 
meridian distances, estimated to the left, must be taken 
with the minus sign. 

The double meridian distance of the last course should 
be equal to the departure of that course. A verification 
of the work is, therefore, obtained by comparing this double 
meridian distance with the departure of the course. 

28. To apply the above rule to the particular example' 
alread} r considered (Art. 21), rule a new table as below,, in 
which are entered the balanced northings and southings, and 
the balanced eastings and westings. 

In this table there is but a single column for the dif¬ 
ferences of latitude, and a single column for the departures. 
The 4- sign shows when the difference of latitude is north, 
and the — sign when it is south. The 4- sign also shows 
when the departure is east, and the — sign when it is west 

8 


114 


ELEMENTS 3F SURVEYING. [BOOK II 


Sta. 

Bearings. 

Distances. 

Dif. Lat. 

Dep. 

D. M. D. 

1 

N 31J° W 

10. 

+ 8.71 

-5.24 

+ 17.91 

— 7.43 

— 5.24 






+ 5.24 

t 

2* 

N G2f° E 

9.25 

+ 4.40 

+ 8.21 

8.21 

o 

o 

S 36° E 

7.60 

-6.01 

+ 4.46 

+ 8.21 
+ 8.21 
+ 4.46 

4 

S 45 £° W 

10.40 

-7.10 

-7.43 

+ 20.88 

+ 20.88 
+ 4.46 
— 7.43 






+ 17.91 


We see, from inspecting the notes, that 2 is the most 
westerly, and 4 the most easterly station. Either of them 
may, therefore, be taken for the principal station. Let ns 
assume 2 for the principal station, and distinguish it by a 
star, thus * 

Haying done so, we enter the departure- 8.21 in the 
column of double meridian distances, which gives the 
double meridian distance of the first course. The double 
meridian distances of the other courses are calculated ac¬ 
cording to the rule; and as the last, opposite to station 1, 
is equal to the departure of the course, the work is known 
to be right. 

29. Haying shown the manner of computing the double 
meridian distance of each course, we shall now deduce a 
rule for finding the 

AREA. 

% 

Let us still consider the same 
example. We will first write the 
differences of latitude and the 
iouble meridian distances of the 
courses, in the following table. 




N 
































THE AREA. 


116 


SEC. III.] 


r 

Stations. 

Dif. of Latitude. 

D. M. D. 

Area. 

+ 

Area. 

1 

+ cB 

+ 2 ba 

2 cAB 


2* 

+ Bs 

+ 2qp 

2BsC 


3 

-yD 

+ 2 nh 


2ms CD 

4 

~Df 

4- 2 ed 


2cmDA 


It is evident, that cB multiplied by 2ba = cA , will give 
double the area of the triangle cAB. But cB and ba are 
both plus; hence, the product will be plus, and must be 
put in the column of plus areas. Double the area of 
the triangle BsC, is equal to Bs multiplied by 2 qp, which 
product is also plus. 

The area of the trapezoid ms OB is equal to yD = ms 
multiplied by nh (Geom., Bk. IY., Prop. VII., S.); hence, 
double the area is equal to yD into 2 nh. But since yD is 
minus, and 2 nh plus, it follows that the product will be 
negative; hence, it must be placed in the column of nega¬ 
tive areas. 

Double the area of the trapezoid cADm , is equal to 
Df= me multiplied by 2 de: but, since Df is negative and 
2 de positive, the product will be negative. 

It is now evident that the difference between the two 
columns is equal to twice the contents of the figure A BCD: 
and since the same may be shown for any other figure, we 
may write, for finding the areas, the following general 


RULE. 

I. Multiply the double meridian distance of each course oy 
its northing or southing , observing that like signs in the multi¬ 
plicand and multiplier give plus in the product , and that un¬ 
like signs give minus in the product. 

II. Place all the products which have a plus sign , in one 
column , and all the products which have a minus sign , in an¬ 
other. 

III. Add up the columns separately and take the difference 
of their sums: this difference will be double the area of the land. 





















[16 ELEMENTS OF SURVEYING-. [BOOK II 

SO. We will now make the calculations in numbers, 
Having balanced the work, we can place it in the follow 
mg table. 


SUv. 

Bearings. 

Dist. 

Dif. Lat. 

Dep. 

D. M. D. 

Area. 

+ 

Area. 

1 

N 3110 w 

10. 

+ 8.71 

— 5.24 

+ 5.24 

45.6404 


2* 

N 62*o e 

9.25 

+ 4.40 

+ 8.21 

8.21 

36.1240 


3 

S 360 e 

7.60 

— 6.01 

+ 4.46 

+ 20.88 


125.4888 

4 

S 45io W 

10.40 

— 7.10 

— 7.43 

+ 17.91 


127.1610 


81.7644 

252.6498 


81.7644 

2)170.8854 

Area in square chains .... 85.4427 

Dividing by 10 . 8.54427 

4 

2717708 

40 

An*. 8A. 2 R. 7 P . 7.08320 

Observing in the field notes that station 2 is the most 
westerly point of the land, we assume the meridian which 
passes through this point, as the one from which the me¬ 
ridian distances are to be calculated. We mark the prin¬ 
cipal station with a star. 

Opposite station 2, we enter, in the column of double 
meridian distances, headed D. M. D., the departure of the 
course from 2 to 8, which is the double meridian distance 
of that course, and plus. To this we add the departure 
of the course, and also the departure of the next course: 
their sum is the double meridian distance of the course 
from 3 to 4. 

To the last sum add the departure opposite station 3, 
and the minus departure opposite station 4: their algebraic 
sum is the double meridian distance from 4 to 1. 

To the last sum add the last departure, which is minus, 
also the next departure which is likewise minus: this will 
give the double meridian distance of the course from 1 to 
2, which is equal to its departure. 

Then forming the products, adding them together, ta¬ 
king their difference, and dividing it by 2, according to 
the rule, we obtain the contents of the ground. 































SEC. Ill] 


OF PLOTTING. 


117 


OF PLOTTING. 


31. It only remains to make 
a plot of the ground. 

For this purpose, draw any 
line, as NS, to represent the me¬ 
ridian passing through the princi¬ 
pal station; and on this line take 
any point, as A, to represent that 
station. 


N 



FIRST METHOD. 

Having fixed upon the scale on which the plot is to be 
made, lay off from B on the meridian, a distance Bs equal 
to the difference of latitude of the first course, and at s 
erect a perpendicular to the meridian, and make it equal 
to the departure of the first course: then draw BC\ which 
will be the first course. 

Through O draw a meridian, and make Cf equal to the 
difference of latitude of the second course, and through / 
draw a perpendicular fD, and make it equal to the depar¬ 
ture of the second course: draw CD } and it will be the 
second course. 

Lay down, in the same manner, the courses DA and 
AB , and the entire plot will be completed. 

SECOND METHOD. 

The work may be plotted in another manner, thus 
At the principal station A, lay off an angle equal to th< 
bearing from B to (7, which will give the direction of BC . 
Then, from the scale of equal parts, make BC equal to the 
first course, this will give the station C. 

Through C draw a meridian, and lay off an angle equal 9ft ' 
to the bearing from C to H, and then lay off the course 
CD. Do the same for the bearing at D and the course 
DA ; also, for the bearing at A and the course AB, and a 

$ 


/ 








118 




# 


ELEMENTS OF SURVEYING. [BOOK IL 

complete plot of the ground will thus be obtained. If the 
work is all right, the last line AB will exactly close the 
figure. This plot is made on a scale of 10 chains to an inch. 

1. It is required to determine the contents and plot of a 
niece of land, of which the following are the field notes, viz. 


Stations. 

Bearings. 

Distances. 

1 

N 46J° W 

20 ch. 

2^ 

N 51f° E 

13.80 

3 

E 

21.25 

4 

S 56° E 

27.60 

5 

S 33i° W 

18.80 

6 

1ST 74*° W 

30.95 


CALCULATION. 


Sta¬ 

tions. 



Dif. 

Lnt. 

Dep. 

BALANCED. 




Bearings. 

Dis. 

N 

+ 

s 

E 

+ 

W 

Lat. 

Dep. 

D.M.D. 

+ 

AREA. 

+ 

AREA. 

1 

N 4Gi° W 

20 ch 

13.77 



1451 

+13.88 

—14.56 

14 56 

202.0928 


2* 

N 51$° E 

13.80 

8.54 


10.84 


+8.61 

+10.81 

10.81 

93.0741 


3 

E 

21.25 



21.25 



+21.20 

42.82 



4 

S 56° E 

27.6!) 

.** 

15.44 

22.88 


—15.29 

+22.82 

86.84 


1327.7836 

5 

S 33p W 

18.80 


15.72 


10.31 

— 15.63 

—10.36 

99.30 


1552.0590 

6 

N 74i° W 

30.95 

8.27 



29.83 

+8.43 

—29.91 

59.03 

497.6229 


Cun 

ofcourses 132.40 

30.58 

31.16 

30.58 

54.97 
54 65 

54.65 




792.7898 2879.8426 
792.7898 


Error in northing .. 0.58 0.32 Error in Westing 2)2087.0528 


j9iis. 104./3 1/2 16P. 1043.5204 

Plot of the example. 
























































i 


»E 0. 11L] PROBLEMS. H9 

32. Remark. When a bearing is due east or west, the 
error in latitude is nothing; the course must then be sub¬ 
tracted from the sum of the courses, and the remainder 
taken in balancing the columns of latitude. In the last 
example, the 3d bearing is due east, and the first term of 
the several proportions for error in latitude, was 132.40 — 
21.25 = 111.15. 

In like manner, if a bearing is due north or south, the 
error in departure is nothing; and the sum of the courses 
must be diminished bj this course, before balancing the 
columns of departure. 

2. Required the contents, and plot of a piece of land, 
of which the following are the field notes. 


Stations. 

Bearings. 

— - -— - 

Distances. 

1 

S 34° W 

3.95 ch. 

2 

S 

4.60 


S 36J-° E 

8.14 

4 ' 

N 59i° E 

3.72 

5 

N 25° E 

6.24 

6 

JN T 16° W 

^ 3.50 

7 

N 65° W 

8.20 


Ans. 10./1. OR. bP. 


3. Required the contents and plot of a piece of land, 
from the following field notes. 


Stations. 

Bearings. 

Distances. 

1 

S 40° W 

70 rods 

2 

1ST 45° W 

89 • 

3-V 

N 36° E 

125 

4 

N 

54 

5 

S 81° E 

186 

6 

S 8° W 

137 

7 

W 

130 


V 


Ans. 207 A. SR. 33 P. 





















120 ELEMENTS OF SURVEYING. [BOOK II 

* 

4. Kequired the contents and plot of a piece of iaml, 
from the following field notes. 


Stations. 

Bearings. 

Distances. 


o 

rH|M 

o 

in 

31.80 ch. 

2 

1ST 54° E 

2.08 

3 

N 29i° E 

2.21 

4 

N 28J° E 

35.35 

5 

1ST 57° W 

21.10 

6 

S 47° W 

81.30 


Ans. 92 A. 3 R 32P. 


5. Kequired the area of a survey of which the follow 
ing are the field notes. 


Stations. 

Bearings. 

Distances. 

1 

1ST 42° E 

5.00 ck 

2 

East. 

4.00 

3 

N9 C E 

4.00 

4 

S 69° E 

5.56 

5 

* S 86° E 

7.00 

6 

S 42° W 

4.00 

7 

S 75° W 

10.00 

8 

N 39° W 

7.50 

_ 


If, in this example, we assume 1 as the principal sta 
tion, the double meridian distances will all be plus, and 
the positive area will exceed the negative. 

In balancing we shall find the error in southing to be 
.28 ch. and in westing .22 cli. The area is 18 A. OB. 11 P. 
It should however be remarked, that in all the examples 
the answers may be slightly varied by distributing the 
corrections. 

0. What is the area of a survey of which the following 
are the field notes. 























SEC. Ill] 


PROBLEMS. 


121 


Stations. 

Bearings. 

Distances. 

1 

N 75° 00' E 

54.8 rods. 

2 

1ST 20° 30' E 

41.2 

3 

East. 

64.8 

4 

S 83° 80' W 

141.2 

5 

S 76° 00' W 

64.0 

0 

North. 

36.0 

7 

IS 

o 

o 

o 

00 

GO 

46.4 

8 

N 58° 15' W 

46.4 

9 

N 36° 45' B 

76.8 

10 

N 22° 80' E 

56.0 

11 

S 76° 45' E 

48.0 

12 

S 15° 00' W 

43.4 

13 

S 16° 45' W 

40.5 


In this survey 4 is the most easterly and 9 the most 
westerly station. The area is equal to 110A. 2 E. 23 P. 
It may vary a little, on account of the way in which the 
balancing is done. 

7. What are the contents of a piece of land of which 
the following are the field notes? 


Stations. 

Bearings. 

Distances. 

1 

S 75° w 

13.70 ch. 

2 

S 20J° W 

10.30 

3 

W est. 

16.20 

4 

N 33i° E 

35.30 

5 

N76° E 

16.00 

6 

South. 

9.00 

7 

N 84° E 

11.60 

8 

S 53i° E 

11.60 

9 

S 36f° W 

19.20 

10 

S 22J° W 

14.00 

11 /> 

N 76f° W 

12.00 

12 

N 15° E 

10.85 

13 

N 16|° E 

10.12 















122 


ELEMENTS OF SURVEYING 


[BOOK IL 


In this survey 4 is the most westerly station and 9 the 
most easterly. The area is 11CL4. 2 R. 23 P. The result 
may, however, as in the other examples, be slightly varied 
by the balancing. 

8. What is the area of a survey of which the following 
are the notes? 


Stations. 

Bearings. 

4 

Distances. 

1 

S 46 J° E 

80 rods 

2 

S 51f° W 

55.20 

3 

West. 

85 

4 

N 56° W 

110.40 

D 

N 331° E 

75.20 

6 ‘ 

S 74£° E 

123.80 


Ans 104 A. 1R 16R 


a 


I. To determine the contents and houndary of a piece of land , 
by means of offsets from the principal lines. 

33. An offset is a line measured perpendicular to 
course, and may lie either on the right or left of it. 

Let AECDE be a piece of 
ground to be surveyed. Let us 
suppose it to be bounded on the 
west and north by a fence and 
road, and on the east and south 
by a creek or river. 

Assume as stations the prin¬ 
cipal points A, B, G\ D, and E. 

Take, with the compass, the bear¬ 
ings from A to B, from B to C, 
from' C to D, from D to A, and 
from E to A ; and measure the dis¬ 
tances AB , BG\ CD , DE ) and EA. 

At convenient points of the course AB, as a, c, and f 
measure the offsets ah, cd , fg. Then, having measured 
these lines, as also the distances Aa, ac , cf and fB , enough 
















SEC. III.] 


PROBLEMS. 


123 


will be known to determine the area which lies without the 
station line AB. The points b, d and g, of the fence which 
runs from A to B, are also determined. 

Erect, in a similar manner, offsets to the other courses, 
and determine the areas which lie without the station lines. 
These several areas being added to the area within the 
station lines, will give the entire area of the ground. 

If the offsets fall within the station lines, the corres¬ 
ponding area must be subtracted from the area which is 
bounded by the station lines. 

II. To determine the bearing and distance from one point to 
another, when the points are so situated that one cannot be 
seen from the other. 

34. Let A and C be the two 
points, and AB a meridian pass¬ 
ing through one of them. From 
either of them, as A, measure a 
course A 2, of a convenient length 
in the direction towards C, and 3 
take the bearing with the com¬ 
pass. At 2, take the bearing of 
a second course, and measure the 
distance to 3. At 3, take a third 
bearing and measure to 4. At 
4, take the bearing to C\ and 
measure the distance from 4 to C. 

Then, the difference between the sum of the northings 
and the sum of the southings will be represented by AB, 
and the difference between the sum of the eastings and 
the sum of the westings by BC. The base AB, and the 
perpendicular BC of the right-angled triangle ABC, are then 
known. The angle at the base, BAG, is the bearing from 
A to O ; or the equal alternate angle at C is the bearing 
from C to A, and the hypothenuse A C is the distance. 

35. Having measured the bearings and courses on the 
field, form a table, and find the base and perpendicular 
of the right-angled ti’angle, in numbers. 






124 


ELEMENTS OF SURVEYING. [BOOK II 


Stations. 

Bearings. 

Distances. 

N. 

s. 

E. 

w. 

1 

N 61° W 

40 ch 

19.89 



34.98 

2 

N 42° W 

41. 

80.47 



27.43 

8 

1ST 12° E 

16.10 

15.75 


8.35 


4 

. 

N 47° E 

82.50 

22.16 


23.77 




AB 

= 87.77 


27.12 

62.41 


27.12 

CB= 35.29 ciL 


"Remark. Had any of the 
courses run south, AB would have 
been equal to the sum of the 
northings, minus the sum of the 
southings. 

To find the angle BAG, or the 
bearing from A to C. 

As radius : tan A : : AB : BO, 
or AB : BG : : R : tan A : 
that is, 



As AB 87.77- . ar. comp. 

: BG 85.29 . 


tan A 21° 54' 12" 


8.056654 

1.547652 

10 . 

9.604806 


To find the distance AC. 
As sin A 21° 54' 12" ar. comp. 

• ...... 

: : BG 35.29 .... 

: AG 94.6 . . . . 


\ 

0.428242 

10 . 

1.547652 

1.975894 


Hence, the bearing and distance are both found. 


OF SUPPLYING OMISSIONS IN THE FIELD NOTES. 

86. The last problem affords an easy method of finding 
the bearing and length of one of the courses of a survey 

































SEC. Ill] 


PROBLEMS. 


125 


✓ 


when the bearings and lengths of all the others are known. 
It may be necessary to use this method when there are 
obstacles which prevent the measuring of a course, or when 
the bearing cannot be taken. Indeed, two omissions may 
in general be supplied by calculation. It is far better, 
however, if possible, to take all the notes on the field. 
For, when any of them are supplied by calculation, there 
are no tests by which the accuracy of the work can be as¬ 
certained, and all the errors of the notes affect also the 
parts which are supplied. 


1. In a survey .we have the following notes: 


Stations. 

Bearings. 

Distances. 

1 

N 31i° W 

10 ch. 

2 

N 62 r E 

9.25 

3 

Lost. 

Lost. 

4 

S 45}° W 

10.40 


What is the bearing and distance from station 3 to 4 ? 

a j Bearing, S 38° 52' E. 
1lS ' ( Distance, 7.03 ch. 


2. In a survey we have the following notes: 


Stations. 

Bearings. 

Distances. 

1 

S 40J° E 

31.80 ch. 

2 

N 54° E 

2.08 

3 

Lost. 

Lost. 

4 

FT 28f° E 

35.35 v ■ 

5 

N 57° W 

21.10 

6 

S 47° W 

31.30 


What is the bearing and distance from 3 to 4? 

Avs i Bearil 'g. N 34 ° 47 ' E ' 
l Distance, 2.19 ch. 





















[26 ELEMENTS OF SURVEYING. [BOOK II 

III. 7b determine the angle included between any two courses. 

when their bearings are known. 

0 

37. Let NS be a meridian 
passing through A. 

Let AB, A (7, AH, AD, and 
AF\ be five courses running 
from A. We readily deduce 
the following 

S 


N 



PRINCIPLES. 


AC is N 26° W 
AII is N 65° W 

CAH= 39° 


When the meridional letters 
are alike, and those of depar 
ture also alike, the difference oj 
the bearings is the-angle between 
the courses. 


AB is N 46° E 
AC is N 26° W 

CAB = 72° 


When the meridional letters 
are alike, and those of depar¬ 
ture unlike, the sum of the bear - 
ings is the angle between the 
courses. 


AC is N 26° W 
AD is S 66° W 

CAD = 180°- 92°= 88° 


When the meridional letters 
are unlike, and those of depar¬ 
ture alike, the angle between the 
courses is equal to 180°, minus 
the sum of the bearings. 


AC is N 26° W 
AF is S 66° E 

CAF= 180°— 40°= 140° 


When the meridional letters 
are unlike, and those of depar¬ 
ture also unlike, the angle be¬ 
tween the courses is equal to the 
difference of the bearings taken 
from 180°. 


Remark. The above principles are determined, under the 
supposition that the two courses are both run from the 
angular point. Hence, if it be required to apply them to 









SEC. Ill] 


OF DIVIDING LAND. 


127 


two courses run in the ordinary way, as we go around the 
field, the bearing of one of them must be reversed before 
the calculation for the angle is made. 

1. The bearings of two courses, from the same point, 
are N 37° E, and S 85° W: what is the angle included 
between them ? 

Am. 132°. 

2. The bearings of two adjacent courses, in going round 
a piece of land, are N 39° W, and S 48° W: what is the 
angle included between them? 

Am. 87°. 

3. The bearings of two adjacent courses, in going round 
a piece of land, are S 85° W, and N 69° W: what is the 
angle included between them? 

Am. 154°. 

4. The bearings of two adjacent courses, in going round 
a piece of land, are 1ST 55° 30' E, and S 69° 20' E : what 
is the angle included between them? 

Am. 124° 50'. 

OF DIVIDING LAND. 

38. Fields are so variously shaped that it is difficult 
to give rules that will apply to all cases. It is by practice 
alone that facility is obtained in that branch of survey¬ 
ing relating to the division of estates. We shall add only 
a few examples that may serve as general guides in the 
application of the principles of Plane Geometry to such 
cases as may arise. 

T. To run a line from the vertex of a triangular field which 

shall divide it into two parts , having to each other the 

ratio of M to N. 

39. Let ABC be any triangular field. 

Divide the side BC into two 

parts, such that (Geom., Bk. IV., 

Prob. 1.) 

BD : DC : : rn : n ; 
and draw the line AD: 

then will. ABD : DAC : : m : n. 


A 






128 


ELEMENTS OF SURVEYING. 


[BOOK II. 


For, the two triangles ABB , ABO having the same alti¬ 
tude are to each other as their bases (Greom., Bk. IV., P. 6, 
C.): hence, the triangle is divided into parts having the 
ratio of m to n. 


II. To run a line parallel to one side of a triangular field , 
that shall form with the parts of the two other sides a 

triangle equivalent to the —part of the field. 

40. Let CBA represent a triangular field and CA the 
side joarallel to which the dividing line is to be drawn. 


On the side BC describe 
a semicircle: then divide BC 
at B, so that 

BB : BO : : m : n. 



At B, erect th; perpendicular BG to the diameter BO, 
and draw BG. Then, with A as a centre, and BG as a 
radius, describe the arc of a circle cutting BO at E. 
Through E draw EF parallel to OA, and it will divide the 
triangle in the required ratio. 

For, (Greom., Bk. IV., P. 23.) 

M' =BE' = BCx BB : 


BB 


or, BE — BC~ X gQ ; whence, 

BE 2 : BO 2 : : BB : BO : : m : n. 
But, since the triangles BEF, BOA are similar, 

: : BEF 


BE 


BO' 


BOA. 


Wherefore, from equality of ratios, 

BEF : BOA : : m 


n ; 


and 


m 

BEF= -~xBOA. 
/1 


Remark. The points E and F may easily be found 
by computation. 


For, since BE' = BCx BB, and BB-~xBC 

n ’ 











OF DIVIDING LAND. 


129 


SEC. 11 LI 


we have 


BE' = BG' 1 x-; or BE=BG 



Tn like manner 


BF= BA 



EXAMPLE. 

Let it be required to divide the trian¬ 
gular field CAB, in wliicli AC=9 ch. AB — 

11 ch. and CB — 7 ch. into two such parts 
that ADE shall be one-fourth of the whole 
field. 

In this case, we have 

m = 1 n = 4, and \f^ = = \ : 

v n 4 2 

hence, AE=4: ch. 50 1. and AD = 5 ch. 50 1. 

III. To run a line from a given point in the houndary of a 
piece of land , so as to cut off, on either side of the line , 
a given portion of the field. 

41. Make a complete survey of the field, by the rules 
already given. Let us take, as an example, the field whose 
area is computed at page 118. That field contains 1044 
li? MSP, and the following is a plot of it. 




Let it now be required to run a line from station A f 
in such a manner as to cut off on the left any part of the 

field; say, 26A 2 R 31 P. 

9 








130 ELEMENTS OF SURVEYING (BOOK II 

It is seen, by examining the field, that tlie division line 
will probably terminate on tne course CD. Therefore, draw 
a line from A to C, which we will call the first closing 
line. 

The bearings and lengths of the courses AD, DC, are 
always known; and in the present example are found in 
the table on page 118: hence, the bearing and distance 
from G to A, can be calculated by Art. 35: they are in 
this example, 

Bearing S 9° 28' E : Course 22.8 ch. 

'Having calculated the bearing and length of the closing 
line, find, by the general method, the area which it cuts 
off: that area, in the present case, is 

13 A 3 R 3 P. 

It is now evident that the division line must fall on 
the right of the closing line AC, and must cut off an area 
A Cff, equal to the difference between that already cut off. 
and the given area: that is, an area equal 

26A 2it 3IP given area, 

13A 3 R 3 P area already cut off, 

to . . . 12A 3 R 28 P. 

Since the bearing of the next course CD, and the bear¬ 
ing of the closing line AC are known, the angle A CD 
which they form with each other, can be calculated, and is 
in this example 80° 32°. Hence, knowing the hypothenuse 
AC, and the angle ACC at the base, the length AG of 
the perpendicular let fell on the course CD, can be found, 
and is 22.19 chains. 

Since the area of a triangle is equal to its base multi¬ 
plied by half its altitude, it follows, that the base is equal 
to the area divided by half the altitude. Therefore, if the 
rea 

12A SR 28P 

be reduced to square chains, and divided by 11.24J chains, 
which is half the perpendicular A G, the quotient, which is 
11.58 chains, will be the base CH. Hence, if we lay off 
from C, on CD, a distance CH, equal to 11.58 chains, ond 





SEC. IV.] 


PUBLIC LANDS. 


131 


then run the line AH,\ it will cut off from the land the re¬ 
quired area. 

Remark I. If the part cut off by the first closing line, 
should exceed the given area, the division line will fall on 
the left of AC. 

Remark II. If the difference between the given 
area and the first area cut off, divided by half the per¬ 
pendicular AG , gives a quotient larger than the course 
CD; then, draw a line from A to D, and consider it as 
the first closing line, and let fall a perpendicular on DE. 

Remark III. When the point from which the divi¬ 
sion line is to be drawn, falls between the extremities 
of a course, dividing the course into two parts, con¬ 
sider one of the parts as an entire course, and the other 
as forming a new course, having the same bearing. The 
manner of making the calculation will then be the same 
as before. 


SECTION IV. 

PUBLIC LANDS—VARIATION OF THE NEEDLE. 

1. Soon after the organization of the present govern 
ment, several of the states ceded to the United States large 
tracts of wild land, and these, together with the lands since 
acquired by treaty and purchase, constitute what is called 
the public lands, or public domain. Previous to the year 
1802, these lands were parcelled out without reference to 
any general plan, in consequence of which the titles often 
conflicted with each other, and in many cases, several grants 
covered the same premises. 

In the year 1802, the following method of surveying 
the public lands, was adopted by Colonel Jared Mansfield, 
then surveyor-general of the North-Western Territory. 

2. The country to be surveyed is first divided by 
meridians, six miles distance from each other; and then 



132 


ELEMENTS OF SURVEYING. [BOOK II. 


again, by a system of east and west lines, also six miles 
from eacli other. The country is thus divided into equal 
squares, which are called townships. Hence, each township 
is a square, six miles on a side, and contains thirty-six 
square miles. 

3. For the purpose of illustration, we have obtained 
from the general land office the accompanying map, which 
represents a considerable portion of the State of Arkansas 

The principal meridian in this Survey is called the 5th 
meridian, and passes through the point of junction of the 
White river and the Mississippi. The principal base line, 
running east and west, intersects this meridian a little to the 
east of White river; and from the meridian and base line, 
reckoned from this point of intersection, all the ranges of 
townships are laid off. 

For example, 1 North, will apply to all the townships 
lving in the first row north of the base line : 1 South, will 
apply to all the townships in the first row south of the base 
line. Kange 1 East, will apply to all the townships lying 
in the first row, east of the 5th meridian : and range 1 
West, will apply to all lying in the first row to the west 
of it. The small figures designate the rows of townships, 
reckoned north and south from the base line, and the 
ranges reckoned east and west from the 5th meridian. 
Thus, township 1 North, range 4 West, has its exact place 
designated, and may be immediately located. 

4. The principal meridians, and the principal base lines 
are established by astronomical observation, and the lines 
of subdivision run with the compass. 

For convenience in making surveys, and for the purpose 
of designating particular localities, a state or large tract, is 
often divided into parts called “ Districts.” There are three 
such districts in the map before us, the boundaries of which 
are designated by the full dark lines. 

5. Each township is divided into equal squares, bv me- 
lidians one mile apart, and by east and west lines at the 
*ame distance from each other. Hence, each township is 
divided into 36 square miles, each one of which is called 



































































































































































































































































































































134 ELEMENTS OF SURVEYING. [BOOK IL 

a section. The sections of a township are numbered from 
1 to 86, beginning at the north-east angle, and each con- 
u,r .s 640 acres 

The diagram exhibits the 36 sections of a township. 


\ 


6 

5 

4 

3 

2 

i- 

7 

8 

9 

10 

11 

12 

18 

17 

16 

15 

14 

13 

19 

20 

21 

22 

23 

24 

30 

29 

28 

27 

26 

25 

31 

32 

33 

34 

35 

36 


To describe a section accurately, we say, section num¬ 
ber 5, in township number 4 north, in range 8d west of a 
known meridian; the one, for example, drawn through the 
mouth of White river. The description fixes precisely the 
place of -the section. Go to the 3d range of townships, 
west of the known meridian, find township number 4 north, 
in this range, and lastly, section number 5 of that town¬ 
ship. The corners of the sections should be marked by 
permanent corner-posts, or by lines blazed on trees. 

6. The sections are divided into half sections, quarter 
sections, and even into eighths of sections. The following 
table shows the contents of a township, and its, subdivi¬ 
sions : 


1 township = 36 sections = 23040 acres. 
1 section = 640 acres. 

\ section = 320 acres. 
i section = 160 acres, 
section = 80 acres. 

















SEC. IV.] VARIATION OF THE NEEDLE. 


135 


VARIATION OF THE NEEDLE. 

7. The angle which the magnetic meridian makes with 
the true meridian, at any place on the surface of the earth, 
is called the variation of the needle at that place, and is east 
or west, according as the north end of the needle lies on 
the east or west side of the true meridian. 

8. The variation is different at different places, and 
even at the same place it does not remain constant for any 
length of time. The variation is ascertained by comparing 
the magnetic, with the true meridian. 

9. If we suppose a line to be traced through those 
points on the surface of the earth, where the needle points 
directly north, such a line is called the line of no variation. 
At all places lying on the east of this line, the variation 
of the needle is west; at all places lying on the west of 
it, the variation is east. 

10. The public is much indebted to Professor Loomis, 
for the valuable results of many observations and much 
scientific research, on the dip and variation of the needle, 
contained in the 39th and 42d volumes of Silliman’s 
Journal. 

The variation at each place was ascertained for the year 
1840 ; and by a comparison of previous observations and 
the application of known formulas, the annual motion, or 
change in variation, at each place, was also ascertained, and 
both are contained in the tables which follow. 

11. If the annual motion was correctly found, and con¬ 
tinues uniform, the variation at any subsequent period can 
be ascertained by simply multiplying the annual motion 
by the number of years, and adding the product, in the 
algebraic sense, to the variation in 1840. It will be ob¬ 
served that all variations west are designated by the plus 
sign ; and all variations east, by the minus sign. The an¬ 
nual motions being all west, have all the plus sign. 


136 ELEMENTS OF SURVEYING. [BOOK II 

12. Our first object will be to mark the line, as it was 
in 1840, of no variation. For this purpose we shall make 
a table of places lying near this line. 


PLACES NEAR THE LINE OF NO VARIATION. 


Place. 

Latitude. 

Longitude. 

Variation. 

An. Motion. 

A Point. 

o 

o 

53' 

OO 

O 

o 

13' 

0° 

00' 

+ 4'.4 

Cleveland, O. 

41 

31 

81 

45 

-0 

19 

4.4 

Detroit, Mich. 

42 

24 

82 

58 

-1 

56 

4 

Mackinaw. 

45 

51 

84 

41 

-2 

08 

3.9 

Marietta, O. 

39 

30 

81 

28 

-1 

24 

4.3 

Charlottesville, V a. 

39 

02 

78 

30 

+ 0 

19 

3.7 

Charleston, S. C. 

32 

42 

80 

04 

-2 

44 

1.3 


At the point whose latitude is 40° 53', longitude 80° 
13', the variation of the needle was nothing in the year 
1840, and the direction of the line of no variation, traced 
north, was 1ST 24° 35' west. The line of no variation, pro¬ 
longed, passed a little to the east at Cleveland, in Ohio— 
the variation there being 19 minutes east. Detroit lay still 
further to the west of this line, the variation there being 
1° 56' east; and Mackinaw still further to the west, as 
the variation at that place was 2° 08' east. 

The course of the line of no variation, prolonged south¬ 
erly, was S 24° 35' E. Marietta, in Ohio, was west of this 
line—the variation there being 1° 24' east. Charlottesville, 
in Virginia, was a little to the east of it—the variation there 
being 19' west; whilst Charleston, in South Carolina, was on 
the west,—the variation there being 2° 44' east. 

From these results, it will be easy to see about where 
the line of no variation is traced in our own country. 

13. We shall give two additional tables: 













SEC. IV.] VARIATION OF THE NEEDLE. 


1*37 


PLACES WHERE THE VARIATION WAS WEST. 


Places. 

Latitude. 

Longitude. 

Variation. 

An. Motion. 

Angle of Maine. 

CO 

o 

00' 

67° 

37' 

+ 19° 

30' 

+ 8'.8 

Waterville, Me. 

44 

27 

69 

32 

12 

36 

5.7 

Montreal. 

45 

31 

73 

35 

10 

18 

5.7 

Keesville, N. Y. 

44 

28 

73 

32 

8 

51 

5.3 

Burlington, Vt. 

44 

27 

73 

10 

9 

27 

5.3 

Hanover, 1ST. H. 

43 

42 

72 

14 

9 

20 

5.2 

Cambridge, Mass. 

42 

22 

71 

08 

9 

12 

5 

Hartford, Ct. 

41 

46 

72 

41 

6 

58 

5 

Newport, R. I. 

41 

28 

71 

21 

7 

45 

5 

Geneva, N. Y. 

42 

52 

77 

03 

4 

18 

4.1 

West Point. 

41 

25 

74 

00 

6 

52 

4 

New York City. 

40 

43 

71 

01 

5 

34 

3.6 

Philadelphia. 

39 

57 

75 

11 

4 

08 

3.2 

Buffalo, N. Y. 

42 

52 

79 

06 

1 

37 

4.1 


PLACES WHERE THE VARIATION WAS EAST. 


Places. 

Latitude. 

Longitude. 

Variation. 

An. Motion. 

Mouth of Colum -) 








bia Eiver. ) 

46° 

12' 

123° 

30' 

-21° 

40' 

Unknown. 

Jacksonville, Ill. 

39 

43 

90 

20 

8 

28 

4- 2'.5 

St. Louis, Mo. 

38 

37 

90 

17 

8 

37 

2.3 

Nashville, Tenn. 

36 

10 

86 

52 

6 

42 

2 

Louisiana, at 

29 

40 

94 

00 

8 

41 

1.4 

Mobile, Ala. 

30 

42 

CO 

GO 

16 

7 

05 

1.4 

Tuscaloosa, Ala. 

33 

12 

87 

43 

7 

26 

1.6 

Columbus, Geo. 

32 

28 

85 

11 

5 

28 

2 

Milledgeville, u 

33 

07 

83 

24 

5 

07 

2.4 

Savannah, “ 

32 

05 

81 

12 

4 

13 

2.7 

Tallahassee, FI. 

30 

26 

84 

27 

5 

03 

1.8 

Pensacola, “ 

30 

24 

87 

23 

5 

53 

1.4 

Logansport, Ind. 

40 

45 

86 

22 

5 

24 

2.7 

Cincinnati, O. 

L- 

39 

06 

84 

27 

4 

46 

3.1 





































13 8 ELEMENTS OF SURVEYING. [BOOK II. 

METHODS OF ASCER1 MINING THE VARIATION. 

r 

14. The best practical method of determining the true 
meridian of a place, is by observing the north star. If this 
star were precisely at the point in which the axis of the 
earth, prolonged, pierces the heavens, then, the intersection^ 
of the vertical plane passing through it and the place, with 
the surface of the earth, would be the true meridian. But, 
the star being at a distance from the pole, equal to 1° 30 ; 
nearly, it performs a revolution about the pole in a circle, 
the polar distance of which is 1° 30': the time of revo¬ 
lution is 23 h. and 56 min. 

To the eye of an observer, this star is continually in 
motion, and is due north but twice in 23 h. 56 min.; and 
is then said to be on the meridian. Now, when it departs 
from the meridian, it apparently moves east or west, for 5 
h. and 59 min., and then returns to the meridian again. 
When at its greatest distance from the meridian, east or west, 
it is said to be at its greatest eastern or western elongation. 

The following tables show the times of its greatest 
eastern and western elongations : 

EASTERN ELONGATIONS. 


Days. 

Ap 

ril. 

May. 

June. 

July. 

August. 

Sept. 


H. 

M. 

H. 

M. 

H. 

M. 

II. 

M. 

II. 

M. 

H. 

M. 

1 

18 

18 

16 

26 

14 

24 

12 

20 

10 

16 

8 

20 

7 

17 

56 

16 

03 

14 

00 

11 

55 

9 

53 

7 

58 

13 

17 

34 

15 

40 

13 

35 

11 

31 

9 

30 

tj 

i 

36 

19 

17 

12 

15 

17 

13 

10 

11 

07 

9 

08 

7 

15 

25 

16 

49 

14 

53 

12 

45 

10 

43 

8 

45 

6 

53 


WESTERN ELONGATIONS. 


Days. 

Oct. 

Nov. 

Dec. 

Jan. 

Feb. 

March. 


H. 

M. 

II. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

H. 

M. 

1 

18 

18 

16 

22 

14 

19 

12 

02 

9 

50 

8 

01 

7 

17 

56 

15 

59 

13 

53 

11 

36 

9 

26 

7 

38 

13 

17 

34 

15 

35 

13 

27 

11 

10 

9 

02 

7 

16 

19 

17 

12 

15 

10 

13 

00 

10 

44 

8 

39 

6 

54 

25 

_ 

16 

49 

14 

45 

12 

34 

10 

18 

8 

16 

6 

33 

_ 





































SEC. IV.] VARIATION OF THE NEEDLE. 


•139 


The eastern elongations are put down from the first 
of Ap.ul to the fiist of October j and the western, from the 
first oi Ootobei to the first of .April j the time is computed, 
from 12 at noon. The western elongations in the first case, 
and the eastern in the second, occurring in the daytime, 
cannot be used. Some of those put down are also invisi¬ 
ble, occurring in the evening, before it is dark, or after day¬ 
light in the morning. In such case, if it be necessary to de¬ 
termine the meridian at that particular season of the year, 
let 5 h. and 59 min. be added to, or subtracted from, the time 
of greatest eastern or western elongation, and the observ¬ 
ation be made at night, when the star is on the meridian. 

15. The following table exhibits the angle which the me¬ 
ridian plane makes with the vertical plane passing through 
the pole-star, when at its greatest eastern or western elon¬ 
gation : such angle is called the azimuth. The mean angle 
only is put down, being calculated for the first of July of 
each year: 

AZIMUTH TABLE. 


Year. 

Lat. 32° 

Azimuth. 

Lat. 34° 

Azimuth. 

Lat. 36° 

Azimuth. 

Lat. 38° 

Azimuth. 

Lat. 40° 

Azimuth. 

Lat. 42° 

Azimuth. 

Lat. 44° 

Azimuth. 

1851 

1° 45}' 

1° 48' 

1° 50}' 

1° 53*' 

1° 56}' 

2° 00}' 

2° 04}' 

1852 

1° 45' 

1° 47*' 

1° 50' 

1° 53' 

1° 56}' 

1° 59}' 

2° 03}' 

1853 

i 

1° 44J' 

1° 47' 

1° 49}' 

1° 52}' 

1° 55}' 

1° 59}' 

2° 03}' 

1854 

1° 44*' 

_ 

1° 46}' 

1° 49}' 

1° 52' 

1° 55}' 

1° 59' 

2° 02}' 

1855 

1° 43?' 

1° 46}' 

1° 48}' 

1° 51}' 

1° 54}' 

1° 58}' 

2° 02}' 

1856 

1° 431' 

1° 45}' 

1° 48}' 

1° 51}' 

1° 54}' 

1° 58' 

2° 01}' 

1857 , 

1° 43' 

1° 45}' 

1° 48' 

1° 50}' 

1° 54' 

1° 57}' 

2° Oil' 

1858 

1° 42 i' 

1° 44}' 

r 47*' 

1° 50}' 

1° 53}' 

1° 57' 

O 

O 

o 

CN 

1859 

1° 42' 

1° 44*' 

1° 47' 

1° 49}' 

1° 53' 

1° 56}' 

2° 00}' 

1860 

1° 41}' 

1° 44' 

i 

1° 46*' 

1° 494' 

A 

1° 52}' 

1° 56' 

2° 00' 

1861 

i 

1° 41}' 

1 

i° 43?': 

1 

1° 46]' 

1" 49' 

1' 52}' 

1° 55f ' 

i 

i° so* ; 

.j 

































































































































140 ELEMENTS OF SURVEYING. [BOOK II 

The use of the above tables, in finding the true meri¬ 
dian, will soon appear. 


TO FIND THE TRUE MERIDIAN WITH THE THEODOLITE. 

16. Take a board, of about one foot square, paste white 
paper upon it, and perforate it through the centre; the 
diameter of the hole being somewhat larger than the diam¬ 
eter of the telescope of the theodolite. Let this board be 
so fixed to a vertical staff, as to slide up and down freely: 
and let a small piece of board, about three inches square, 
be nailed to the lower edge of it, for the purpose of hold¬ 
ing a candle. 

About twenty-five minutes before the time of the great¬ 
est eastern or western elongation of the pole-star, as shown 
by the tables of elongations, let the theodolite be placed 
at a convenient point and levelled. Let the board be 
placed about one foot in front of the theodolite, a lamp or 
candle placed on the shelf at its lower edge; and let the 
board be slipped up or down, until the pole-star can be 
seen through the hole. The light reflected from the paper 
will show the cross hairs in the telescope of the theodolite. 

Then, let the vertical spider’s line be brought exactly 
upon the pole-star, and, if it is an eastern elongation that 
is to be observed, and the star has not yet reached the 
most easterly point, it will move from the line towairds the 
east, and the reverse when the elongation is west. 

At the time the star attains its greatest elongation, it 
will appear to coincide with the vertical spider’s line for 
some time, and then leave it, in the direction contrary to 
its former motion. 

As the star moves towards the point of greatest elonga¬ 
tion, the telescope must be continually directed to it, by 
means of the tangent-screw of the vernier plate; and when 
the star has attained its greatest elongation, great care 
should be taken that the instrument be not afterwards 
moved. 

Now, if it be not convenient to leave the instrument in 
its place until daylight, let a staff, with a candle or small 


SEC. IV.J VARIATION OF THE NEEDLE. 141 

lamp upon its upper extremity, be arranged at thirty or 
forty yards from the theodolite, and in the same vertical 
plane with the axis of the telescope. This is easily effect¬ 
ed, by revolving the vertical limb about its horizontal axis 
without moving the vernier plate, and aligning the staff to 
coincide with the vertical hair. Then mark the point di¬ 
rectly under the theodolite; the line passing through this 
point and the staff, makes an angle with the true meridian 
equal to the azimuth of the pole-star. 

From the table of azimuths, take the azimuth corres¬ 
ponding to the year and nearest latitude. If the observed 
elongation was east, the true meridian lies on the west of 
the line which has been found, and makes with it an angle 
equal to the azimuth. If the elongation was west, the 
true meridian lies on the east of the line: and, in either 
case, laying off the azimuth angle with the theodolite, gives 
the true meridian. 

TO FIND THE TRUE MERIDIAN WITH THE COMPASS. 

17. 1. Drive two posts firmly into the ground, in a line 

nearly east and west; the uppermost ends, after the posts are 
driven, being about three feet above the surface, and the 
posts about four feet apart : then lay a plank, or piece of 
timber three or four inches in width, and smooth on the 
upper side, upon the posts, and let it be pinned or nailed, 
to hold it firmly. 

2. Prepare a piece of board four or five inches square, 
and smooth on the under side. Let one of the compass- 
sights be placed at right angles to the upper surface of the 
board, and let a nail be driven through the board, so that 
it can be tacked to the timber resting on the posts. 

3. At about twelve feet from the stakes, and in the 
diiection of the pole-star, let a plumb be suspended from 
the top of an inclined stake or pole. The top of the pole 
should be of such a height that the pole-star will appear 
about six inches below it; and the plumb should be swung 
in a vessel of water to prevent it from vibrating. 


142 


ELEMENTS 0F SURVEYING 


[BOOK 11 


This being done, about twenty minutes before the time 
of elongation, place the board, to which the compass-sighl 
is fastened, on the horizontal plank, and slide it east oi 
west, until the aperture of the compass-sight, the plumb- 
line, and the star, are brought into the same range. Then 
if the star depart from the plumb-line, move the compass- 
sight, east or west, along the timber, as the case may be, 
until the star shall attain its greatest elongation, when it 
will continue behind the plumb-line for several minutes ; 
and will then recede from it in the direction contrary to 
its motion before it became stationary. Let the compass- 
sight be now fastened to the horizontal plank. During this 
observation it will be necessary to have the plumb-line 
lighted: this may be done by an assistant holding a candle 
near it. 

Let now a staff, with a candle or lamp upon it, be 
placed at a distance of thirty or forty yards from the 
plumb-line, and in the same direction with it and the com¬ 
pass-sight. The line so determined, makes, with the true 
meridian, an angle equal to the azimuth of the pole-star; 
and, from this line, the variation of the needle is readily 
determined, even without tracing the true meridian on the 
ground. 

Place the compass upon this line, turn the sights in the 
direction of it, and note the angle shown by the needle. 
Now, if the elongation, at the time of observation, was 
west, and the north end of the needle is on the west side of 
the line, the azimuth, plus the angle shown by the needle, 
is the true variation. But should the north end of the 
needle be found on the east side of the line, the elon°-a- 
tion being west, the difference between the azimuth and 
the angle would show the variation: and the reverse when 
the elongation is east. 

1. Elongation west, azimuth . . 2° 04' 

North end of the needle on the west, angle 4° 06' 


Variation 6° 10' west. 




SEC. IV.] VARIATION OF THE NEEDLE. 


143 


2. Elongation west, azimuth . . 1 ° 59 ' 

North end of the needle on the east, angle 4° 50' 

Variation 2 ° 51' east. 

3. Elongation east, azimuth . . 2 ° 05' 

North end of the needle on the west, angle 8 ° 30' 

Variation 6 ° 25' west. 

4.. Elongation east, azimuth . . 1 ° 57' 

North end of the needle on the east, angle 8 ° 40' 

_ 

Variation 10° 37' east. 


Remark I. The variation at West Point, in Septem¬ 
ber, 1835, was 6 ° 32' west. 

Remark II. The variation of the needle should al¬ 
ways be noted on every survey made with the compass, 
and then if the land be surveyed at a future time, the old 
lines can always be re-run. 

18. It has been found by observation, that heat and 
cold sensibly affect the magnetic needle, and that the same 
needle will, at the same place, indicate different lines at 
different hours of the day. 

If the magnetic meridian be observed early in the 
morning, and again at different hours of the day, it will 
be found that the needle will continue to recede from the 
meridian as the day advances, until about the time of the 
highest temperature, when it will begin to return, and at 
evening will make the same line as in the morning. This 
change is called the diurnal variation , and varies, during 
the summer season, from one-fourth to one-fifth of a 
degree. 

19. A very near approximation to a true meridian, and 
consequently to the variation, may be had, by remember¬ 
ing that the pole-star very nearly reaches the true meri¬ 
dian, when it is in the same vertical plane with the star 
Alioth in the tail of the Great Bear, ivhich lies nearest the 
foil?' stars forming the quadrilateral. 








144 ELEMENTS OF SURVEYING. [BOOK it 

The vertical position can be ascer¬ 
tained by means of a plumb-line. To 
see the spider’s lines in the field of the 
telescope at the same time with the 
star, a faint light should be placed 
near the object-glass. When the 
plumb-line, the star Alioth, and the 
north star, fall on the vertical spider’s 
line, the horizontal limb is firmly 
clamped, and the telescope brought 
down to the horizon ; a light, seen # 
through a small aperture in a board, 
and held at some distance by an as¬ 
sistant, is then moved according to signals, until it is cov¬ 
ered by the intersection of the spider’s lines. A picket 
driven into the ground, under the light, serves to mark the 
meridian line for reference by day, when the angle formed 
by it and the magnetic meridian may be measured. 





BOOK III. 


LEVELLING AND TOPOGRAPHICAL SURVEYING. 


SECTION I. 

OF LEVELLING. 


1. Levelling is tlic art of determining tlie relative dis¬ 
tances of points from the centre of the earth. 

2. A line whose points are all equally distant from the 
centre of the earth, is called a line of true level , and a sur¬ 
face, all whose points are equally distant from the centre 
of the earth, as the surface of still water, is called a level 
surface. 

3. One point is said to be above another, when it is 
farther from the centre of the earth; and this difference of 
distance from the centre, is called the difference of level be¬ 
tween the two points. 

4. A straight line drawn tangent to a line of true level 
at any point, is a horizontal line, and is called a line of 
apparent level. Thus (Pl. 4, Fig. 1), if G is the centre of 
the earth and AEF a line of true level, ABB is a line of 
apparent level. This is the line of level determined by an 
instrument. The difference between the apparent and true 
level at any distant station i>, as determined from A, is BE, 
or the excess of the secant of the arc AE over the radius.. 

5 . To find a general formula for computing this excess, 
we have (Georn. B. IV., Prop. XXX.) 

Z# 2 = BE {BE + 2 EC ); 

but since the arc AE is very small in comparison with the 

10 




146 


ELEMENTS OF SURVEYING. [BOOK III 


radius of the earth, the arc AE will not differ sensibly from 
the tangent AB; the diameter 2EC may, for the same 
reason, be taken for the secant {BE + 2 EG) : lienee, 

AE~ = BE X2EC, or dividing by 2EC, 


BE — 


AE 


(!)• 


2EG 

Tf we take the mean diameter of the earth to be 7919 

AE 2 

miles, formula (1) gives BE = (2) : hence, 


The departure of the apparent from the true level, starting 
from a given point, is equal to the square of the distance to the 
second point, divided by the diameter of the earth. 

If in formula (2) you give to AE, in succession, every 
value from 1 chain to any given number of chains, (say 
100), and reduce at the same time both terms of the frac¬ 
tion to inches, a table may be computed as below. 

Table showing the differences in inches between the true and apt' 
parent level, for distances between 1 and 100 chains. 


Chains. 

Inches. 

Chains. 

Inches. 

Chains. 

Inches. 

Chains. 

Inches. 

1 

.001 

26 

.845 

51 

3.255 

76 

7.221 

2 

.005 

27 

.911 

52 

3.380 

77 

7.412 

3 

.011 

28 

.981 

53 

3.511 

78 

7.605 

4 

.020 

29 

1.051 

54 

3.645 

79 

7.802 

5 

.031 

30 

1.125 

55 

3.781 

80 

8.001 

6 

.045 

31 

1.201 

56 

3.925 

81 

8.202 

7 

.061 

32 

1.280 

57 

4.061 

82 

8.406 

8 

.080 

33 

1.360 

58 

4.205 

83 

8.612 

9 

.101 

34 

1.446 

59 

4.351 

84 

8.832 

10 

.125 

35 

1.531 

60 

4.500 

85 

9.042 

11 

.151 

36 

1.620 

61 

4.654 

86 

9.246 

12 

.180 

37 

1.711 

62 

4.805 

87 

9.462 

13 

.211 

38 

1.805 

63 

4.968 

88 

9.681 

14 

.245 

39 

1.901 

64 

5.120 

89 

9.902 

15 

.281 

40 

2.003 

65 

5.281 

90 

10.126 

16 

.320 

41 

2.101 

66 

5.443 

91 

10.351 

17 

.361 

42 

2.208 

67 

5.612 

92 

10.587 

18 

.405 

43 

2.311 

68 

5.787 

93 

10.812 

19 

.451 

44 

2.420 

69 

5.955 

94 

11.046 

20 

.500 

45 

2.531 

70 

6.125 

95 

11.233 

21 

.552 

46 

2.646 

71 

6.302 

96 

11.521 

22 

.605 

47 

2.761 

72 

6.480 

97 

11.763 

23 

.661 

48 

2.880 

73 

6.662 

98 

12.017 

24 

.720 

49 

3.004 

74 

6.846 

99 

12.246 

25 

.781 

50 

3.125 

75 

7.032 

100 

12.502 i 







































SEC. I.] 


THE Y LEVEL. 


147 


Observing that for AE= 80 drains = 1 mile, BE is equal 
to 8.001 inches, or about two-thirds of a foot, and since 
the differences of level vary as the squares of the dis 
tances, we have the following easy rule for finding the cor 
rection in feet. 

The correction for curvature , in feet , is equal to two-third, 
of the square of the distance in miles. 

INSTRUMENTS. 

6. Before proceeding further in the discussion of the 
principles of levelling, we will describe some of the in¬ 
struments used, and first, 

THE Y LEVEL. 

7. A level is an instrument used to determine horizontal 
lines, and the difference of level of any two points on the 
surface of the earth. 

The part of the instrument shown in PI. 4, Fig. 2, rests 
on a tripod, to which it is permanently attached at Z. HI1 
Is a horizontal brass plate, through which four levelling 
screws with milled heads are passed, and worked against a 
second horizontal plate GC. Two of these screws, K and 
7, are seen in the figure. S is a clamp-screw, which, being 
loosened, allows the upper part of the instrument to turn 
freely around its axis. Q is a tangent-screw, by means of 
which the upper part of the instrument is moved gently, 
after the clamp-screw S has been made fast. EE is a hori¬ 
zontal bar, perpendicular to which are the wyes, designat¬ 
ed Y’s, that support the telescope LB. This telescope is 
confined in the Y’s by the loops r, r, which are fastened 
by the pins p and p. The object-glass B , is adjusted to 
its focus by the screw AT, tiie eye-glass L slides out and 
in freely. The screws f f work the slide which carries 
the horizontal hair; and two horizontal screws, only one 
of which, a, is seen, work the slide that carries the verti¬ 
cal hair. CD is an attached spirit-level. The screw N 
elevates and depresses the Y, nearest the eye-glass. In 
some instruments this Y is elevated and depressed, bv 
means of two screws at M and R. 


148 


E L E M E NTS OF SURVEYING. [BOOK III. 


Before using this level, it must be adjusted. The ad¬ 
justment consists in bringing the different parts to their 
proper places. 

The line of collimation is the axis of the telescope. With 
this axis, the line drawn through the centre of the eye¬ 
glass and the intersection of the spider’s lines, within the 
barrel of the telescope, ought to coincide. 

First adjustment.* To fix the intersection of the spider’s 
lines in the axis of the telescope. 

Having screwed the tripod to the instrument, extend 
the legs, and place them firmly. Then loosen the clamp- 
screw #, and direct the telescope to a small, well-defined, 
and distant object. Then slide the eye-glass till the spider’s 
lines are seen distinctly; after Avhich, with the screw Aj 
adjust the object-glass to its proper focus, when the object 
and the spider’s lines will be distinctly seen. Hote now 
the precise point covered by the intersection of the spider’s 
lines. 

Having done this, revolve the telescope in the Y’s, half 
round, when the attached level CD will come to the upper 
side. See if, in this position, the horizontal hair appears 
above or below the point, and in either case, loosen the 
one, and tighten the other, of the two screws which work 
the horizontal hair, until it has been carried over half the 
space between its last position and the observed point. 
Carry the telescope back to its place; direct again, by the 
screws at M and i?, the intersection of the spider’s lines to 
the point, and repeat the operation, till the horizontal hair 
neither ascends nor descends while the telescope is revolv¬ 
ed. A similar process will arrange the vertical hair, and 
the line of collimation is then adjusted. 

Second adjustment. To make the axis of the attached 
level CD parallel to the line of collimation. 

Turn the levelling screws M and A, until the bubble 


* This, and some of the following adjustments, are so similar to those of the 
theodolite, that they would not be here repeated, but that some may use the 
level without wishing to study a more complicated instrument. 




SEC I] 


THE Y LEVER. 


14 9 

of the level DC stands at the middle of the tube. Then 
open the loops, and reverse the telescope. If the bubble 
still stands at the middle of the tube, the axis of the level 
is horizontal; but if not, it is inclined, the bubble being 
at the elevated end. In such case, raise the depressed, or 
depress the elevated end, by means of the small screw h, 
half the inclination ; and then with the screws, at M and i?, 
bring the level to a horizontal position. Reverse the teles¬ 
cope in the Y’s, and make similar corrections again ; and 
proceed thus, until the bubble stands in the middle of 
the tube, in both positions of the telescope; the axis of the 
level is then horizontal. 

Let the telescope be now revolved in the Y’s. If the 
bubble continues in the middle of the tube, the axis of the 
level is not only horizontal, but also parallel to the line of 
collimation. If, however, the bubble recedes from the centre, 
the axis of the level is inclined to the line of collimation, 
and must be made parallel to it, by means of two small 
screws, which work horizontally; one of these screws is 
seen at q. By loosening one of them, and tightening the 
other, the level is soon brought parallel to the line of col¬ 
limation ; and then, if the telescope be revolved in the Y’s, 
the bubble will continue at the middle of the point of the 
tube. It is, however, difficult to make the first part of this 
adjustment, while the axis of the level is considerably in¬ 
clined to the line of collimation: for, allowing the level to 
be truly horizontal in one position of the telescope, after it 
is reversed, there will be but one corresponding position 
in which the bubble will stand at the middle of the tube. 
This suggests the necessity of making the first part of the 
adjustment with tolerable accuracy; then, having made the 
second with care, re-examine the first, and proceed thus 
till the adjustment is completed. ^ 

Third adjustment. To make the level CD and the 
line of collimation perpendicular to the axis of the instrument, 
or parallel to the horizontal bar EE. 

Loosen the clamp-screw S, and turn the bar EE\ until 
level DC comes directly over two of the levelling 


150 


ELEMENTS OF SURVEYING. [BOOK IIL 


screws. By means of tliese screws, make tlie level CD 
truly horizontal. Then, turn the level quite round; if, 
during the revolution, it continue horizontal, it must be at 
right angles to the axis of the instrument about which it 
has been revolved. But if, after the revolution, the level 
CD be not horizontal, rectify half the error with the screws 
at M and R, and half with the levelling screws. Then 
place the bar ED over the other two levelling screws, and 
make the same examinations and corrections as before; and 
proceed thus, until the level can be turned entirely around 
without displacing the bubble at the centre. When this 
can be done, it is obvious that the level DC and the line 
of collimation, are at right angles to the axis of the instru¬ 
ment about which they revolve; and since the axis is care¬ 
fully adjusted by the maker, at right angles to the bar EE, 
it follows, that the line of collimation, the level DC J and 
the bar EE, are parallel to each other. 

The level is now adjusted. When used, however, it is 
best to re-examine it every day or two, as the work will 
be erroneous unless the instrument is accurately adjusted. 


THE WATER LEVEL. 


8. The Water Level is an instrument that possesses the 
advantage of never requiring adjustment , and also of being 
very cheap; in fact, any ordinary workman may con¬ 
struct one. Having no telescope, it is impossible to take 
long sights, but for such work as is required to be done 
by the ordinary surveyor, it gives very good results. 

Two brass cups, C and D, about one inch in diam¬ 
eter, and from four to five inches in height, are permanent¬ 
ly attached to a hollow brass tube of three feet long and 




B 


of receiving the 

O 

ends E and F of 



two bottles, the 

bottoms of which have been cut off. The bottoms may be 
cut off by means of a hot iron, or file. The ends are fixed 
in their places with putty. 












SEC. LJ 


LEVELLING STAVES. 


151 


The projecting axis g works in a hollow cylinder h, 
which forms the top of a stanch The tube, when the level 
is required for use, is filled with water (colored with lake 
or indigo), till it nearly reaches the necks of the bottles. 
After placing the stand tolerably level by the eye, with¬ 
draw both corks, and the surface of the water in the bot¬ 
tles will indicate a horizontal line in whatever direction the 
tube is turned. This level is well adapted to tracing con¬ 
tour lines as described in the next section. 


LEVELLING STAVES. 

9. The levelling staves are used to determine the points 
at which a given horizontal line intersects lines that are 
perpendicular to the surface of the earth, and to show the 
distances of such points of intersection from the ground. 

The levelling staff is a necessary accompaniment to 
either of the levels described. Several kinds are used. 

One of the best, consists of a staff 12 or 15 feet long, 
and graduated to feet, tenths, and hundredths. A sliding 
vane is made to move up or down by a 
cord and pulleys, and on the vane is a 
vernier, by means of which the reading 
of the staff may be effected to thou¬ 
sandths of a foot. AB represents a 
portion of the staff, DC the moveable 
vane, with an opening EF\ through which 
the graduation on the staff is seen. F is 
the vernier of the vane, the 0 being de¬ 
termined by the transverse line DC. To 
render this line more distinct, the vane 
is divided into four quarters, and the 
alternate ones are painted black, which, 
by their contrast with the white quar¬ 
ters, show the line DC distinctly. 

10. Another variety of levelling staff is shown in PL 4, 
Fig. 3. It is formed of two pieces, each about six feet 
long, one of which slides in a groove of the other, and 
bears a vane similar to that already described. It is grad¬ 
uated to feet, inches, and eighths of an inch. The line of 


















152 


ELEMENTS OF SURVEYING. [BOOK III 


sight of the telescope is always directed to the centre of 
the vane. When the line of sight is less than six feet from 
the ground, the staff is reversed,—the vane run up the staff, 
and the readings made by means of the reversed figures at the 
right, where they are cut by the lower line of the vane. 
When the line of sight is more than six feet from the ground, 
the staff stands as in the figure, the reading is then made at 
the line be, and the figures indicating the height, are found on 
the sliding part which carries the vane. The reading of the 
staff, as it now stands, is seven feet. 

11. Another rod is sometimes used on which the figures 
are marked so plainly, that they may be read by the ob¬ 
server himself, without the aid of a vane; thus avoiding 
errors through ignorance or negligence of the rodman. 

If the telescope used, inverts the object, the figures should 
be made inverted on the staff, so as to appear erect. Each 
of the rods described, has its advantages, and either one may 
be used according to the circumstances of the survey. 

12. There is a method of testing the adjustments of the 
Y level, which ought not to be neglected, since all the re¬ 
sults depend on the accuracy of the instrument. The 
method is this: 

The level being adjusted, place it at any convenient 
point, as G (Eig. 4). At equal distances of about 100 yards, 
on either side, and in the same line with the level, place 
the levelling staves, CE, BF. Make the level horizontal 
with the levelling screws. Then, turn it towards either 
staff, as BF, and run the vane up or dowm, as required, 
until the intersection of the hairs strikes the centre : then 
make the slide fast, and note carefully the height of the 
vane. Turn the level half round, and do the same in 
respect of the staff CE. 

Let the telescope be now reversed in the Y’s. Sight 
again to the staff BF, and note the exact height of the 
vane. Let the telescope be now turned half round, and 
the same be done for the staff CF. If the two heights 
last observed, are equal to those first noted, each to each, 
the line of collimation is perpendicular to the axis of the 


SEC. I.] 


OF LEVELLING. 


153 


instrument, and if the bubble has, at the same time, pre¬ 
served its place at the middle point of the tube, the instru¬ 
ment is truly adjusted. 

For, had the line of collimation been inclined to the 
axis of the level, it would, in the first instance, have taken 
the direction AF or Ad\ and when turned half round, it 
would have taken the direction AF or Ah. The telescope 
being reversed in the Y’s, and again directed to the stall 
BF\ the line of collimation would take the direction Ad or 
AF : and when turned to the staff CE\ it would take the 
direction Ab or AF: and the two distances BF J Bd, or Cb. 
CE , can only be equal to each other when the line of col 
limation falls on the horizontal line gf 


LEVELLING IN THE FIELD. 

13. The operation of levelling may be undertaken: 

1st. For the purpose of determining the difference oi 
level between two given points. 

2d. For the purpose of obtaining a section or profile 
along a given line, as in the reconnoissance for a line of 
railroad. 

3d. For the purpose of determining the contour lines in 
a topographical survey, as described in the next section. 


DIFFERENCE OF LEVEL BETWEEN TWO POINTS. 

14. When it is proposed to find the difference of level 
of any two objects, or stations, all levels made in the di¬ 
rection of the station at which the work is begun, are 
called, for the sake of distinction merely, back-siglits; and 
levels taken in the direction of the other station, fore¬ 
sights. 

Before going on the field with the level, rule three 
columns, as below, and head them, stations, back-sights, 
fore-sights. 




154 


ELEMENTS OF SURVEYING. [BOOK III 


FIELD NOTES. 


Stations. 

-j- Back-Sights. 

— Fore Sights. 

1 

10 

3 

2 

11-6 

0 

3 

6-8 

4-9 

4 

3-9 

8-3 

Sums . . 

. . . 31-11 

16-0 


16-00 


Dif. of level. 

L. 

. . . 15-11 



EXAMPLE. 

Find the difference of level between any two points , as A and 

G (PI. 4, Fig. 5.) 

The level being adjusted, place it at any point, as B , as 
nearly in the line joining A and G as may be convenient. 
Place a levelling staff at A, and another at A r , a point 
lying as near as may be in the direction of G. Make the 
level horizontal, by means of the levelling screws; turn the 
telescope to the staff at A , and direct the person at the 
staff to slide up the vane until the horizontal line ah pierces 
it« centre; then note the distance Ab (equal to 10 feet in 
the present example), and enter it in the column of back¬ 
sights, opposite station 1. Sight also to the staff at JVj and 
enter the distance Na, equal to 3 feet, in the column of fore¬ 
sights, opposite station 1. 

Take up the level, and place it at some other convenient 
station, as (7, and remove the staff at A, to M. Having 
levelled the instrument, sight to the staff at N, and enter 
the distance Nd, 11 feet 6 inches, in the column of back¬ 
sights, opposite station 2 : sight also to the staff at M y and 
enter the distance Mf equal 0, in the column of fore-sights, 
opposite station 2. 




















SEC. I.J 


OF LEVELLING. 


155 


Let the level be now removed to any other station, as 
D, and the staff at JVJ to some other point, as P. Let- the 
distance Mg, ecpial to 6 feet S inches, be entered in the 
column of back-sights, opposite station 3, and the distance 
Ph, equal to 4 feet 9 inches, in the column of fore-sights. 
Let the instrument be now placed at E\ and the distance 
Pm , equal to 8 feet 9 inches, and Gn, equal to 8 feet 3 
inches, be entered opposite station 4, in their proper 
columns. 

It is evident from the figure, that the difference of level 
NF, between A and N, is equal to the back-sight bA, dim¬ 
inished by the fore-sight aN\ also that the difference of 
level between N and M is equal to the back-sight dlSf, dim¬ 
inished by the foresight 0, and since each set of obser¬ 
vations is entirely independent of every other set, we may 
infer that the difference of level between two points as determin¬ 
ed by one position of the level, is equal to the back-siglit , dim¬ 
inished by the fore-sight. If the fore-sight be greater than the 
back-sight, the difference will be affected with a minus sign, 
a result which shows that the second point is lower than 
the first. Generally, the difference of level between any two 
points , determined as above , is equal to the sum of the back¬ 
sights diminished by the sum of the fore-sights. If the result is 
plus, the second point is higher than the first; if negative, 
it is lower. 

In the example given, the difference of level between 
A and G, is 15 feet 11 inches. 

15. In the previous example, we did not regard the dif¬ 
ference between the true and apparent level. If it be ne¬ 
cessary to ascertain the result with extreme accuracy, this 
difference must be considered: and then, the horizontal 
distances between the level, at each of its positions, and the 
staves, must be measured, and the apparent levels dimin¬ 
ished by the differences of level; which differences can be 
found from the table. 


156 


ELEMENTS OF SURVEYING. [BOOK III 


THE FOLLOWING IS SUCH AN EXAMPLE. 


Stat. 

Back-sts. 

Distances. 

Fore-st. 

Distances. 

Cor.back-sights 

Cor. fore-sts. 

1 

9-8 

20 ch. 

1-6 

32 ch. 

9-7.500 

1-4.720 

2 

8-7 

25 ch. 

2-4 

28 ch. 

8-6.219 

2-8.019 

o 

O 

5-2 

18 ch. 

3-1 

16 ch. 

5-1.595 

8-0.680 

4 

10-3 

29 ch. 

1-9 

87 ch. 

10-1.949 

0-11.538 

5 

11-0 

45 ch. 

2-5 

72 ch. 

10-9.469 

1-10.520 


44-2.782 

9-6.477 


In this example, tlie first column shows the stations; 
the second, the back-sights; the third, the distances from 
the level in each of its positions to the back staff; the 
fourth, the fore-sights; the fifth, the distances from the 
level to the forward staff; the sixth and seventh, are the 
columns of back and fore-sights, corrected by the difference 
of level. The corrections are thus made :—The difference 
of level in the table corresponding to 20 chains, is 5 tenths 
of an inch, which being subtracted from 9 feet 8 inches, 
leaves 9 feet 7.5 inches for the corrected back-sights; this 
is entered opposite station 1 in the sixth column. The dif¬ 
ference of level corresponding to 82 chains, is 1.280 inches, 
which being subtracted from the apparent level, 1 foot 6 
inches, leaves 1 foot 4.720 inches for the true fore-sight 
from station 1. The other corrections are made in the 
same manner. 

The sum of the back-sights being 44 feet 2.732 inches, 
and the sum of the fore-sights 9 feet 6.477 inches, it fol¬ 
lows, that the difference, 34 feet 8.255 inches, is the true 
difference of level. 

16. In finding the true from the apparent level, we 
have not regarded the effect caused by refraction on the 
apparent elevation of objects, as well because the refraction 
is different in different states of the atmosphere, as because 
the corrections are inconsiderable in themselves. 

17. The small errors that would arise from regarding 
the apparent as the true level, may be avoided by placing 




























SEC. I.] 


OF LEVELLING. 


157 


the levelling staves at equal distances from the level. In such 
case, it is plain, 1st, that equal corrections must be made 
in the fore and back-sights; and, 2dly, that when the fore 
and back-sights are diminished equally, the result, which is 
always the difference of their sums, will not be affected. 

This method should always be followed, if practicable, 
as it avoids the trouble of making corrections for the dif¬ 
ference of true and apparent level. 

The differences between the true and apparent level, 
being very inconsiderable for short distances, if only ordi¬ 
nary accuracy be required, it will be unnecessary to make 
measurements at all. Care, however, ought to be taken, 
m placing the levelling staves, to have them at as nearly 
equal distances from the level as can be determined by the 
eye; and if the distances are unequal, let the next distances 
also be made unequal; that is, if the back-sight is the 
longer in the first case, let it be made proportionally 
shorter in the second, and the reverse. 

LEVELLING FOR SECTION. 

18. Having decided upon the line along which a section 
is to be taken, let a permanent mark be made at the be¬ 
ginning of the line: this is called a bench-mark. A bench- 
mark is made by drilling a hole in a rock, or by painting 
upon a rock or fence, or sometimes by driving a stake in 
the ground, with its upper end marked by a nail-head. 
Bench-marks should be made from time to time along the 
line, to serve as checks, in case a re-survey should become 
necessary. 

The operations in the field are similar to those in {he 
last example, and the field notes are kept in the same 
manner, except that a new column is added for bearings, 
when it is necessary to make a plot of the line of survey. 
The total distance of each point above or below the start¬ 
ing point may be computed, and written in a separate col¬ 
umn, paying particular attention to the signs. We annex 
an example, in which the heights are estimated in feet, 
and decimals of a foot. 


ELEMENTS OF SURVEYING. [BOOK IIL 


158 


Sta¬ 

tion. 

Distances in 

feet. 

B. Sight. 

F. Sight. 

Dif. between 

B. S. and F. S. 

Total Dif. of 

Level. 

REMARKS. 

1 

650 

2.35 

14.55 

-12.20 

— 

12.20 

Commenced at ben^h-mark A , 

2 

700 

3.56 

9.58 

- 6.02 

— 

18.22 


3 

750 

10.34 

6.21 

+ 4.13 

— 

14.09 


4 

650 

14.55 

0.25 

+ 14.30 

+ 

0.21 


5 

600 

9.98 

1.67 

+ 8.31 

+ 

8.52 


6 

650 

3.62 

14.54 

-10.92 

— 

2.40 



B.M 

1.23 

13.45 

-12.22 

— 

14.62 

Bench-mark on rock. 

7 

500 

2.23 

12.05 

- 9.82 

— 

24.44 

Terminating at£M on oak tree. 

8 

750 

6.20 

19.55 

-13.35 

— 

37.79 



The fifth column shows the difference of level between 
any two consecutive positions of the levelling staff, and is 
found by subtracting the fore-sight from the corresponding 
back-sight, and giving to the remainder the proper sign. 
The sixth column shows the distance of each point above 
or below the Wnch-mark A, and is obtained by continual 
additions of the numbers in column 5. Thus, 

(- 12.20) + (- 6.02) = - 18.22 ; (- 18.22) + 4.13 = - 14.09; 
and so on. 

It will be seen that the point of termination is 37.79 
feet below the starting point. 

f 

PLOTTING THE SECTION OR PROFILE. 

• 19. The vertical distances being generally very small as 
compared with the horizontal distances, two different scales 
become necessary in plotting a profile. In order that the 
vertical distances may be fully exhibited in the plan, the 
scale used for them is much larger than is used for lines 
measured in a horizontal direction. This becomes absolutelv 
necessary where long lines of profile, with a gentle slope, 
are to be plotted, as is always the case in the trial section 
of a railroad survey. We shall illustrate the manner of 
plotting, by drawing the section determined by the field- 
notes just given. 

20. Draw a horizontal line AK, called a datum line, and 
































SEC. II.] TOPOGRAPHICAL SURVEYING. 


159 


assume some point as A, to represent the point of begin¬ 
ning: lay off on the datum line, distances equal to the 


L 



measured distances 650, 700, 750, &c., feet to IC : using in 
this case a scale of 1500 feet to 1 inch. At the points A, 
(7, D, A, &c., thus determined, erect perpendiculars, making 
them equal, on a scale of 25 feet to the inch, to the cor¬ 
responding differences of level taken from the field-book; 
through the points thus found, draw the irregular line 
APLM y and it will represent the surface of the ground 
along the line of level. 

The bench-mark, between stations 7 and 8, is not plotted, 
as it is supposed to be out of the line of the section, and 
no distances are measured to it. 

*4 


SECTION II. 

TOPOGRAPHICAL SURVEYING. 

21. Besides the surveys that are made to determine the 
area of land and the relative positions of objects, it is fre¬ 
quently necessary to make minute and careful examinations 
for the purpose of ascertaining the form and accidents of 
the ground, and to make such a plan as will distinguish 
the swelling hill from the sunken valley, and the course 
of the rivulet from the unbroken plain. 











160 


ELEMENTS OF SURVEYING. [BOOK III 


22. This branch of surveying is called Topography. In 
surveys made with a view to the location of extensive 
works, the determination of the slopes and irregularities of 
the ground is of the first importance: indeed, the examina¬ 
tions would otherwise be useless. 

23. The manner of ascertaining these irregularities is, to 
suppose the surface of the ground to be intersected by a 
system of horizontal planes at equal distances from each 
other; the curves determined by these secant planes, being 
lines of the surface, will indicate its form at the places of 
section, and, as the planes are nearer or more distant from 
each other, the form of the surface is more or less accu¬ 
rately ascertained. 

If such a system of curves be determined, and then pro¬ 
jected or let fall on a horizontal plane, it is obvious that 
the curves on such plane will be nearer together or farther 
apart, as the ascent of the hill is steep or gentle. 

If, therefore, such intersections be made, and the curves 
so determined be accurately delineated on paper, the map 
will give such a representation of the ground as will 
show its form, its inequalities, and its striking character¬ 
istics. 

24. The subject divides itself, naturally, into two parts. 

1st. To make the necessary examinations and measure¬ 
ments on the field; and, 

2d. To make the delineations on paper. 

For the former of these objects, the theodolite is the 
best instrument; the common level, however, will answer 
all the purposes, though it is less convenient. 

Before going on the field, it is necessary to provide a 
number of wooden stakes, about two feet in length, with 
heads. These stakes are used to designate particular points, 
and are to be driven to the surface of the ground. A 
nail should then be driven into the head of each of them, 
to mark its centre. 

25. We shall, perhaps, be best understood, by giving an 
example or two, and then adding such general remarks as 


SEC II.] TOPOGRAPHICAL SURVEYING. 


161 


will extend tlie particular cases to all others that can 
occur. 

Let A (PL 4, Fig. 6), be the summit of a hill, the con¬ 
tour of which it is required to represent. At A, let a 
stake be driven, and let the axis of the theodolite, or level, 
be placed directly over the nail which marks its centre. 
From A, measure any line down the hill, as AB, using the 
telescope of the theodolite or level to arrange all its points 
in the same vertical plane. Great care must be taken to 
keep the measuring chain horizontal, for it is the horizontal 
distances that are required. At different points of this line, 
as a, h, c, d, &c., let stakes be driven, and let the horizon¬ 
tal distances An, ab, be, and cd , be carefully measured. In 
placing the stakes, reference must be had to the abruptness 
of the declivity, and the accuracy with which the surface 
is to be delineated: their differences of level ought not to 
exceed once and a half, or twice, the distance between the 
horizontal planes of section. 

Having placed stakes, and measured all the distances 
along the line AB, run another line down the hill, as AC, 
placing stakes at the points e, f g, and h, and measuring 
the horizontal distances Ae, ef, fg, and gh. Pun also the 
line AD, placing stakes at i, I, m, and n, and measuring 
the horizontal distances Ai, il, Im, and mn. 

Each line, AB, AC, AD, running down the hill from A, 
may be regarded as the intersection of the hill by a verti¬ 
cal plane; and these secant planes are to be continued over 
all the ground which is to be surveyed. If the work is. 
done with a theodolite, or with a level having a compass, 
the angles DAB and BAG, contained by the vertical se¬ 
cant planes, can be measured; if it is done with a level, 
having no needle, let any of the distances ae, If, ai, 11, &a t 
be measured with the chain, and there will then be known 
the three sides of the triangles Aae, Ahf, Aai, All, &c. 

Let now, the difference of level of the several points 
marked in each of the lines AB, AD, AC, be determined. 

In the present example the results of the measurements 
and levelling, are— 


11 


L 62 


ELEMENTS OF SURVEYING. [BOOK II 1 


Line 

Distances. 

Aa = 40 feet 
ab = 50 “ 

be = 30 “ 
cd = 46 “ 


AB. 

Difference of Level* 

A above a 12 feet 

a above b 8 “ 

5 above c 9 “ 

c above d 11 “ 


Line AC. 


Distances. 

Ae = 28 feet 
ef = 45 “ 

fg = 55 “ 

^ =49 “ 

Line 

Distances. 

Ai =25 feet 
il = 55 “ 
bn =38 “ 
mu = 48 “ 

Angle CAB =25°, 


Difference of Level. 

A above e 11 feet 
e above / 9 u 
f above g 12 “ 

g above h 14 11 

AD. 

Difference of Level. 
A above i 9 feet 
i above Z 13 “ 

l above m 7 11 

m above n 14 “ 

Angle DAB= 30°. 


These data are sufficient, not only to find the intersect 
tions of horizontal planes with the surface of. the hill, but 
also for delineating such curves of section on paper. 

Having drawn on the paper the line AB, lay off the 
angle BAC = 25°, and the angle BAD — 30°. Then, from 
a convenient scale of equal parts, lay off the distances Aa, 
ab, be, cd, Ae, ef fg, gh, Ai, il, bn, and mn. 

Let it be required that the horizontal planes be at a 
distance of eight feet from each other. Since A is the 
highest point of the hill, and the difference of level of the 
points A and a, is 12 feet, the first plane, reckoning down* 
wards, will intersect the line traced on the ground from A 
to B, between A and a. Regarding the descent as uniform, 
which we may do for small distances without sensible error, 
we have this proportion; as the difference of level 'of the 
points A and a, is to the horizontal distance Aa, so is 8 
feet, to the horizontal distance from A to where the first 





SEC. II.l TOPOGRAPHICAL SURVEYING. 


163 


horizontal plane will cut the line from A to B. This dis¬ 
tance being thus found, and laid off from A to o, gives o, 
a point of the curve in which the first plane intersects the 
ground. The points at which it cuts the line from A to C, 
and the line from A to 7), are determined similarly, and 
three points in the first curve are thus found. 

The graphic operations are greatly facilitated by the aid 
of the sector. Let it be borne in mind, that the descent 
from A to a, is 12 feet, and that it is required, upon the 
supposition of the descent being uniform, to find that part 
of the distance corresponding to a descent of 8 feet. Take 
the distance from A to a, in the dividers, and open the 
arms of the sector until the dividers will reach from 12 on 
the line of equal parts, on one side, to 12 on the line of 
equal parts, on the other. Then, without changing the 
angle, extend the dividers from 8 on one side, to 8 on the 
other; this will give the proportional distance to be laid 
off from A to o. Or, if the dividers be extended from 4 
to 4, the proportional distance may be laid off from a 
to o. 

If the distances to be taken from the sector fall too 
near the joint, let multiples of them be used ; as for in 
stance, on the French sectors, let the arms be extended 
until the dividers reach from 120 on the one, to 120 on 
the other, then 80 or 40 will be the proportional numbers. 
Other multiples may be used, though it is generally more 
convenient to multiply by 10. 

26. The second plane is to pass 8 feet below the 'first, 
that is, 16 feet below J., or 4 feet below «, a being 12 feet 
below A. Take the distance ab in the dividers, and ex¬ 
tend the sector, so that the dividers will reach from 8 to 
(the descent from a to b being 8 feet) 8, or from 80 to 
80; then, the distance from 4 to 4, or from 40 to 40, being 
laid off from a to p, gives p, a point of the second curve. 

The difference of level between a and b being 8 feet, 
and the difference of level between a and p being 4 feet, 
the difference of level between p and must also be 4 
feet; hence, the third plane will pas? Vt below b, and 


164 


ELEMENTS OF SURVEYING. [BOOK III. 


determined as above, is a point*of the third curve, and 
so on. After having determined the points in which each 
contour line cuts the lines diverging from A , let the con¬ 
tour lines be drawn through them, so as to indicate the 
surface of the hill. The numbers (8), (16), &c., show the 
vertical distances of the respective planes below the point A. 

i 

27. Having drawn the horizontal curves, the next thing 
to be done is so to shade the drawing that it may represent 
accurately the surface of the ground. This is done by 
drawing a system of small broken lines, as in the figure, 
perpendicular in direction to the horizontal curves already 
described. In all topographical representations of undulat¬ 
ing ground, the lines of shading are drawn perpendicular to 
the horizontal curves. 

A profile along either of the diverging lines may be 
plotted by the rules already given (Art. 20.) The diagram 
shows the profile along the line AB. 



28. The following example will illustrate the methods 
employed in making a topographical survey, where great 
accuracy is required. 

By means of a theodolite or level, range a line of stakes 
A , A, £7, j9, A, &c., along one side, or through the middle of 
the ground to be surveyed, at equal and convenient distances 
from each other, say 50 feet apart. Mark, with a piece of 
red chalk, on each stake in this row, one of the letters of 
the alphabet, A, A, C, JD, E, &c., in their order. At A, 
range a line of stakes, perpendicular to AE ' planting the 
stakes at intervals of 50 feet; and mark them with the 

letters 4’ 4’ 4’ , which are read A first, A second, 

l f O f * 7 | 

A third, &c. 










SEC. IT.] TOPOGRAPHICAL SURVEYING. 


166 


T - - ■ « 

A 

—----*■ 

A 

'A 

A 

A 

l 

z 

3\ 

4 

s 


' v 






' .... \ T 








B 

B 

B 

B 

2*1 

1 

Or 

3 

4 

5 

< 

• 






b 


ty, 

c 

c 

a 

C 

C 

2 

z 

3 

4 

& 











* - 






tP A 




n 

D 

J) 

n 

D 

i 

z 


4 

6 


p ''V 






a 



El 

Ez 

E3 

El 

Es 


A & /?, range a line of stakes also perpendicular to AE, 
and at distances of 50 feet from each, other, and designate 

them ^ &c. Do the same at G. D, E, &c., until all 

the stages are placed, dividing the area to be surveyed 

into squares of 50 feet on a side. The letters and figures 

should be plainly marked on a smooth face of each stake, 
for facility of reference. If this system of notation be fol¬ 
lowed, the stakes may be recorded without danger of con¬ 
fusion. 

The next operation is to determine the difference of 
level between each stake, and some fixed horizontal plane, 
which is called a 'plane of reference. If the sea is near, the 

plane of mean low water, may be taken as the plane of 

reference. If not, assume the horizontal plane, passing 
through the lowest point of the ground to be surveyed, and 
make a permanent bench-mark at the point of beginning. 
If the lowest point cannot be easily determined, assume 
such a plane of reference as shall pass quite below the low¬ 
est point of the ground. 

In the example, which we have taken for illustration, 
the stoke ^ is at the lowest point, and let us assume tha 
plane of reference to pass through that point. 









ELEMENTS OF SURVEYING. [ROOK Ill 


1 6G 

Set up the level at some convenient point, as a, take the 

reading of a levelling staff, set up at ^ and enter this 

reading as a back-sight. Then take the readings of the 
staff, at as many stakes as can be reached from the posi¬ 
tion a of the level, entering them as fore-sights. Endeavor¬ 
ing to make the last reading as small as possible. At this 

last stake ^ drive a small peg for a bench-mark. 

Move the level to a second point ft, and take a back¬ 
sight to the bench-mark (CT), and fore-sights, to as many 
stakes as possible. The following is the form of a field- 
book, used in topographical levelling. 

FIELD NOTES. 


Back- 

-sights. 

Fore- 

Sights. 

Difference 

Total dif.of level 

above E 3 

Remarks. 

Object 

Reading 

Object 

Reading 



Object 

Reading 








E3 

0.000 


E3 

11.432 

1)3 

1.211 

+ 10.221 

D3 

10.221 




C4 

0.897 

+ 

0.314 

C4 

10.535 

Check 10.535 

C4 

11.112 

E2 

5.281 

+ 

5.831 

E2 

16.366 




E4 

6.154 

— 

0.873 

E4 

15.493 




D4 

C.D01 

+ 

0.153 

D4 

15.646 




D2 

1.182 

+ 

4.819 

D2 

20.465 




C3 

2.917 

— 

1.735 

C3 

18.730 




B5 

G.080 

— 

3.163 

B5 

15.567 




C5 

0.'921 

+ 

5.159 

C5 

20.726 




B4 

0.113 

+ 

0.808 

B4 

21.534 

Check 10.999 

B4 

11.882 

El 

8.019 

+ 

3.863 

El 

25.397 

21.534 



B3 

3.990 

+ 

4.029 

B3 

29.426 




Dl 

4.118 

— 

0.12S 

Dl 

29.298 




C2 

1.880 

+ 

2.233 

C2 

31.536 




A4 

5.000 

— 

3.120 

A4 

28.416 




A5 

9.928 

— 

4.923 

A5 

23.438 




Do 

1.675 

+ 

8.253 

D5 

31.741 




E5 

1.111 

+ 

0.564 

E5 

32.305 




A3 

0.108 

+ 

1.003 

A3 

33.308 




Cl 

0.004 

+ 

0.104 

Cl 

33.412 

Check 11.878 

Cl 

1U149 

B2 

4.181 

+ 

6.968 

B2 

40.380 

33.412 



Bl 

2.008 

+ 

2.173 

Bl 

42.553 




A2 

0.817 

+ 

1.191 

A2 

43.744 

Check 10.332 









43.744 

A2 

10.102 

A1 

4.332 

+ 

5.770 

Al 

49.514 

Check 5.770 









49.514 

































REC. II.] TOPOGRAPHICAL SURVEYING 107 

If we subtract tlie first fore-sight (D3), from the back¬ 
sight (E3), the difference, entered in the column headed 
difference, is evidently the height of (Do), above the plane 
of reference through (E3); and we accordingly enter it 
under the column headed total cliff, of level , as well as in 
the column of differences. If we subtract the fore-sight 
(C4) from the fore-sight (D3), the difference, entered in the 
column of difference, is evidently the height of (C4) above 
(D3); if we now add this difference to the previous total, 
we shall find the height of (C4) above (E3). Subtracting 
the fore-sight (E2) from the back-sight (C4), we get the dif¬ 
ference of level between (E2) and (C4) which, added to the 
previous total, gives the height of (E2), above the stake 
(E3). In subtracting the fore-sight (E4) from the fore-sight 
(E2), we find a negative result which shows that (E4) is 
below (E2). We enter, then, this difference with its neg¬ 
ative sign, and to get the total, we subtract this difference 
from the previous total, and so on. 

As a check on the accuracy of our computation, sub¬ 
tract the fore-sight (C4) from the baek-siglit (E3), and the 
difference will give the height of (C4), above the plane of 
reference. 

Again, subtract the fore-sight (B4) from the back-sight 
(04), and add the remainder to the height of (C4,) and we 

shall find the height of (B4), which should agree with the 

height found under the heading, total cliff, of level; and so 
on for each time the level is moved. 

PLOTTING THE WORK. 

29. Draw, on a piece of paper, a straight line AK 
From a scale of equal parts, set off distances AB , BG. 
&c., each to represent 50 feet. Erect perpendiculars at 
each of the points A, B, 0.\ &c., and then set off the distan¬ 
ces from A to 2, from 2 to 3, &c., each to represent 50 

feet; and through the points 2, 3. 4 and 5, draw parallels 

to AE. These, by their intersections with the lines drawn 
through A, B, C , &c., will determine the position of the 

stakes, ^ A, an( I write in red ink on the plot, the 

i, '-'i 


168 


ELEMENTS OF SURVEYING. 


[BOOK III 


height above the plane of reference of each stake, taken fiom 
the column of total differences in the field-book. Let- us sup¬ 
pose that the horizontal planes are to be taken at distances 
of 6 feet We may find the points in which the contour 



lines intersect the lines at right angles, by the previous 
method, or perhaps still better, let the Surveyor take the 
plot thus commenced into the field, and by the eye trace 
the contour lines on the map. If we note where the lines 
at right angles cut fences, roads, streams, &c., we can, by 
joining the points,- obtain a plot of the ground. 

80. The contour lines may be found as follows: Set up 
the level at a, and observe that the back-sight, to the stake, 
placed at (Eo), gave a reading of 11.432. Depress the 
vane equal to the distance between the horizontal secant 
planes, that is, 6 feet, which is done by placing it at the 
reading 5.432. Then direct the rodman, by signals up or 
down the hill, till the horizontal hair of the telescope coin¬ 
cides with the horizontal line of the vane. The foot of the 
staff is then 6 feet above the first point. Let a stake, 
marked 6, be driven here, and direct the rodman around 
the hill, until a second position shall be found, when the 

























SEC. II.] TOPOGRAPHICAL SURVEYING. 


169 


horizontal hair of the telescope will cut the vane, and drive 
vhere another stake, marked 6; and so on, until a sufficient 
number of stakes have been driven to determine the curve 
(6). Then, let the line of stakes, marked 6, be surveyed 
with the compass and chain, and plotted. Other contour 
ines may be found in a similar manner. 


31. We will add another example for determining the 
contour of an undulating piece of ground (PI. 4, Fig. 
7,) by means of horizontal sections. Let rows of stakes 
DA , HE\ IF, &c., be driven at intervals, depending upon 
the required accuracy of the survey, and let f, g, h, &c., 
be stakes driven along the lines, at such points as w: 
best show the accidents of ground. Determine as before 
the difference of level between each stake, and some fixed 
point, and then determine where the contour lines cut the 
lines AD, Eli, &c., by the rules already laid down. 

After the stakes are all placed, and the distances meas 
ured, let the differences of level of all the points so desig 
nated be found. In the present example, the results of the 
measurements are, 


Ft. 

Act = 80 

AE— 100 

Ft. 

EF — 100 

Ft. 

EG = 100 

ab = 60 

Ef = 105 

Fi = 74 

Gm— 96 

be = 90 

fid = 85 

ik = 115 

mn = 76 

cd — 55 

rH 

L- 

II 

Id = 60 

'O 

II 

—7 

02 

dD - 50 

1- 

II 

fc| 

II = 86 

r- 

00 

II 


Of the Levelling. 


Line AD. 

Line EH. 

Line FI. 

Line GL. 

Ft. 

Ft. 

Ft. 

Ft. 

A above Cl 5 

E below A 3 

F below E 2 

G below F 1 

a u b 6 

E above J 9 

F' above X 3 

G above m 2 

b “ cl 

/ “ <7 3 

i “ h 5 

m u n 1 

c below d 2 

g 11 h 1 

k “ 1 2 

n “ p 2 

d above D 4 

Jl below H 3 

l below I 3 

p e«ow Ij 4 


GB = 100 
Bq = 76 
qs — 85 
st = 127 
tQ = 47 


Line B G. 

Ft. 

B below G 2 
B above q 3 

q “ s 2 
5 “ t 3 

t below 0 5 


The heights of the points are here compared with each 
other, two and two. Before, however, we can conceive 












iro 


ELEMENTS OF SUPVEYING. [BOOK TIL 


clearly their relative heights, we must assume some one 
point, and compare all the others with it. Let the point 
A be taken. The height of 





Ft. 




Ft. 




Ft. 




Ft. 

A above a 

5 

A above / 

12 

A abov 

qIc 

13 

A above p 

11 

A 

a 

b 

11 

A 

u 

9 

15 

A 

ii 

l 

15 

A 

ii 

L 

7 

A 

a 

C 

18 

A 

ii 

h 

16 

A 

ii 

I 

12 

A 

ii 

B 

8 

A 

ll 

d 

16 

A 

It 

H 13 

A 

u 

a 

6 

A 

ii 

9 

11 

A 

u 

B 

20 

A 

ll 

F 

5 

A 

ii 

m 

8 

A 

ii 

s 

13 

A 

u 

E 

3 

A 

ll 

i 

8 

A 

ii 

n 

9 

A 

ii 

t 

16 


.And of A above G ' 11 feet. 


This being done, a mere inspection shows us the high¬ 
est and lowest points, as also the relative heights of the 
others, reckoning upwards or downwards. Let them be 
now written in the order of their heights above the lowest 
point, which is 1). The difference of level between A and 
B being 20 feet, if the difference of level of each of the 
points below A, be taken from 20 feet, the remainder will 
be the height above B. Arranging them in their order, 
we have 





Ft 




Ft. 




Ft. 




Ft. 

c 

above 

J) 

2 

IF 

ibov 

e D 

7 

P 

above I) 

9 

B above B 

12 

d 

u 

B 

4 

k 

ii 

1) 

7 

9 

ti 

I) 

9 

L 

u 

B 

13 

h 

ll 

B 

4 

s 

ii 

I) 

7 

G 

a 

B 

9 

G 

ii 

B 

14 

t 

li 

D 

4 

f 

ii 

D 

8 

n 

a 

B 

11 

a 

ii 

B 

15 

9 

ll 

D 

5 

I 

it 

I) 

8 

i 

ii 

* I) 

12 

F 

it 

B 

15 

l 

ll 

I) 

5 

b 

ii 

D 

9 

m 

ii 

B 

12 

E 

ii 

B 

17 


A above j 0, 20 feet. 


In this example, the plane of reference is assumed 
through i), the lowest point of the ground; and the secant 
planes are taken 3 feet apart. 

82. The manner of shading the map, so as to indicate 
the hills and slopes, consists in drawing the lines of shad¬ 
ing perpendicular to the horizontal curves, as already ex 
plained. These shading lines are drawn close together, 
when the slope is abrupt, and further apart, as it grows 
more gentle. Fig. 7 indicates the method of shading. 






SEC TI.] TOPOGRAPHICAL SURVEYING. 


171 


oo. W lien the plane of reference is so chosen that the 
points of the work fall on different sides of it, all the re¬ 
ferences on one side are called positive, and those on the 
other, negative. The curves having a negative reference 
are distinguished by placing the minus sign before the 
number; thus —( ). 

84. In topographical surveys, great care should be taken 
to leave some permanent marks , with their levels written 
on them in a durable manner. For example, if there are 
any rocks, let one or more of them be smoothed, and the 
vertical distance from the plane of reference marked there¬ 
on: or let the vertical distance of a point on some promi¬ 
nent building, be ascertained and marked permanently on 
the building. Such points should also be noted on the 
map, so that a person, although unacquainted with the 
ground, could by means of the map, go upon it, and trace 
out all the points, together with their differences of level. 

35. Besides representing the contour of the ground, it 
is often necessary to make a map which shall indicate the 
cultivated field, the woodland, the marsh, and the winding 
river. For this, certain characters, or conventional signs, 
have been agreed upon, as the representatives of things, 
and when these are once fixed in the mind, they readily 
suggest the objects for which they stand. Those which 
are given in Plates 5 and 6, have been adopted by the 
Engineer Department, and are used in all plans and maps 
made by the United States Engineers. 

It is very desirable that a uniform method of deline¬ 
ation should be adopted, and none would seem to be of 
higher authority than that established by the Topographi¬ 
cal Bureau. It is, therefore, recommended, that the con¬ 
ventional signs given in Plates 5 and 6, be carefully 
studied and uniformly followed. 


BOOK I Y. 


GEODESIC, TRIGONOMETRIC AND MARITIME 

SURVEYING 


SECTION I. 

GEODESIC AND TRIGONOMETRIC SURVEYING. 

1. When a large extent of territory, or a long line of 
sea-coast is to be surveyed, it becomes necessary to con¬ 
sider the curvature of the eartli’s surface; this branch of 
surveying is called Geodesic surveying. 

2. Extensive geodesic operations prove that the earth 
is an oblate spheroid, the shortest diameter of which coin¬ 
cides with the terrestrial axis, and all of whose meridians, 
are equal ellipses. The meridian lines, however, differ so 
little from the circumferences of circles, that they may be 
taken for them, except when great accuracy is required. 
The earth, will, therefore, in the following pages, be re¬ 
garded as a perfect sphere. 

3. The operations necessary to the successful execution 
of a Geodesic Survey, require the minutest attention, and 
when performed, numerous corrections are to be applied to 
the measured lines and angles, on account of the various 
causes of error incident to such operations. 

To investigate those causes of error, and to deduce rules 
for correcting the errors, in all cases, would far exceed 
the limits of an elementary treatise,. We shall, therefore, 
attempt nothing more than a brief outline of the operations 



SEC. L] 


TRIANGULATION. 


173 


of a trigonometric survey, with the application of some of 
the more important corrections. 

4. It may be observed that most of the operations de- 
scrib-ed in this section, are equally applicable, whether we 
regard the area surveyed as plane or spherical: in either 
case, the basis of an accurate survey, is an extensive sys¬ 
tem of triangulation. 

5. After having made a preliminary examination or re¬ 
connaissance of the territory to be surveyed, suitable stations 
are selected at the most prominent points, and these points 
are marked by staves or signals. 

A base line is then measured. The length of the base 
will, in general, depend upon the magnitude of the survey, 
and each extremity is marked by a signal. 

The next step is the triangulation. At each extremity 
of the base, the angles between the base, and the lines 
drawn to each of the visible signals, are carefully meas¬ 
ured by means of a theodolite. The sides of the triangles 
thus obtained, serve as new bases upon which other trian¬ 
gles may be formed, and so on, until the entire area is 
covered by a net-work of triangles. 

6. This system of triangles is called the primary system, 
and the operation of forming them is called the primary 
triangulation. Within the primary triangles, and depending 
upon them, a system of smaller triangles is formed in the 
same manner, called the secondary system; and if the extent 
or importance of the work should demand it, the secondary 
may be sub-divided into tertiary triangles. 

Having completed the triangulation, the characteristics 
of the surface, such as roads, streams, villages, boundaries, 
&c., are filled in by means of the compass, plain table, or 
some of the methods already explained. 

After the field work is completed, the triangles, when 
regarded as spherical, are reduced by applying the formula 
for spherical excess, hereafter explained, and other neces¬ 
sary corrections, and thus the whole work is plotted upon 
paper. 


174 


ELEMENTS OF SURVEYING. [BOOK II 


PRELIMINARY RECONNOISSANCE AND ESTABLISHMENT OF 

SIGNALS. 

7. Before commencing a trigonometrical survey, aj ex 
animation of the entire territory should be made for the 
purpose of selecting a location for the base line, and proper 
points for stations; this examination should be more or 
less elaborate, according to the nature and extent of the 
survey. 

The proper distribution and combination of the trian¬ 
gles, so as to adapt them to the survey in hand, require 
great judgment and care, and but few rules can be given for 
the selection of trigonometrical points. Those points should, 
in general, be chosen in such a manner, that they may be 
distinctly visible from each other, and so that the triangles 
formed, by uniting them, may be as nearly as possible 
equilateral. 

It is easily seen, that a triangle which has an obtuse 
or a very acute angle, will experience a greater change of 
form for a given error, than one which is nearly equilate¬ 
ral ; and since the accuracy of each triangle depends upon 
the preceding ones, it is further evident, that the introduc¬ 
tion of a single ill-conditioned triangle, might vitiate the 
whole survey. Except in extreme cases, no angle, less than 
30°, should be used, and even angles of 80° should not be 
admitted when the locality can be so chosen as to prevent 
it. The base is usually much shorter than the sides of the 
primary triangles; these sides, however, should be increased 
as rapidly as is consistent with the above remarks. 

8. The accompanying diagram will illustrate the man¬ 
ner of increasing the sides without introducing ill-con¬ 
ditioned triangles. Having measured the base AB, and the 
requisite angles, the triangles ABO and ABB , may be de¬ 
termined, and the line DC computed; with DC as a base, 
the triangles DCE and DCF are formed, and thence EIIF,\ 
and EGF , in which the sides are much greater than the 
base AB. 


SEC. I.] 


SIGNALS. 


175 



F 

In this manner the sides may be increased to any de¬ 
sirable extent. An ordinary map of the country, or a 
sketch made with the pocket compass, will be of material 
assistance in making a proper distribution of the stations. 

9. The stations are marked by signals, which may be 
constructed in a great variety of ways, depending upon the 
locality of the stations, and the lengths of the sides of the 
triangles. 

Sometimes a signal has to be raised above the level of 
the adjacent country, in which case it is constructed of 
timbers, and upon the apex, is placed a vertical staff, bear¬ 
ing a flag. The exact trigonometrical point is determined 
by a plumb-line, suspended from the apex of the signal. 

A temporary signal may be constructed with three or 
four pieces of scantling framed and traced, k 

as shown in the annexed figure, with a short 
pole projecting from the apex. The plumb 
determines the point Z?, which is the exact trig¬ 
onometrical point over which the theodolite 
is to be placed. Where the sides of the trian¬ 
gles are not very great, a pole, planted ver¬ 
tically, and surmounted by a flag, will an¬ 
swer as a signal. 

In order to distinguish the different signals, the fiags 
which they bear, should be different from each other. 
They may be formed by arranging stripes cf white and 







176 


EL EM Em-a uF SURVEYING. 


[BOOK TV. 


red, according to some pre-arranged plan, and tlie Hags of 
the different stations should be entered in a book. For 
the purpose of future reference, the trigonometrical point, 
at each station, as A, should be indicated by a permanent 
mark. If the point falls upon a rock, a hole may be drill¬ 
ed to show the locality; or if not, a mark-stone may be 
gunk under the point, deep enough to be beyond the reach 
of accident. A record of the monument should be pre¬ 
served, together with its reference to some of the perma¬ 
nent objects in the neighborhood. 

In order to render the signals visible from the distant 
stations, polished _ tin plates are sometimes attached to the 
signal-post, so as to reflect the sun towards the stations at 
certain hours of the day. The Drummond-light has also 
been used to show very distant stations. A light may also 
be produced that can be seen at a distance of 60 or 70 
miles, by placing a ball of lime about a quarter of an inch 
in diameter, in the focus of a parabolic reflector, and heat¬ 
ing it intensely by a stream of oxygen gas, directed by a 
blow-pipe, through a flame of alcohol. If obstacles, as trees, 
and under-brush intervene, vistas have to be opened along 
the lines, from station to station. 


MEASUREMENT OF A BASE LINE. 

10. The measurement of a base line on which the ac 
curacy of the entire survey depends, is one of the most 
difficult operations of geodesic surveying, and one, for the 
successful accomplishment of which, art and science have 
been strongly taxed. The selection of a proper site for a 
base line, forms one of the first objects of the preliminary 
reconnaissance. Ii> should, if pQssible, be fixed on an open 
plain. It must be so chosen, that the surrounding signals 
may be distinctly seen from its extreme points; and hence, 
those signals which mark points of the adjacent triangula 
tion, should be selected with reference to the base. The 
length, of the base , should, in a measure, depend upon the 
magnitude of the survey, though circumstances seldom 
admit its being taken more than 6 or 8 miles in length. 


S E 0. 1] 


BASE LINE. 


177 


11. Different instruments have been used for measuring 
base lines, such as steel chains, glass, platinum and deal 
rods; and more recently, a combination of rods, of differ¬ 
ent metals, so adjusted, that the apparatus maintains an in¬ 
variable length at all temperatures. This last mentioned 
apparatus, has been much improved, and most successfully 
used by Prof. Bache, in the Survey of the United States 
Coast. 

12. In minor surveys, where the base line does not 
much exceed 1000 or 2000 feet, sufficient accuracy may be 
attained by the use of wooden rods. To render the rods 
less susceptible of change, from moisture, they should be 
saturated with boiling oil, and covered with a thick coat¬ 
ing of varnish. 

The ends of the rods should be protected by metallic 
caps, which prevent their wearing, and insure a more per¬ 
fect contact. 

When the rods are prepared for use, they should be 
carefully compared with some standard measure, and from 
time to time this comparison should be repeated, in order 
to detect any minute change of length, should such change; 
take place. 

13. The following method of measuring a base line of 
1000 or 2000 feet, may be rendered very accurate. 

Having decided upon the direction of the base, and 
measured it carefully, two or three times with a chain, let 
a theodolite be planted at one end of the line, and direct¬ 
ed upon a flag, planted at the other. Then, by means- of 
the vertical limb, let a row of pickets be driven along the 
base, taking care to plant them at a distance from each* 
other, equal to the length of one of the deal rods. Then, 
plant in the place of each picket, a vertical post, 6 or 8 : 
inches in diameter, and projecting a sufficient distance- 
above the surface of the ground. If necessary, let the 
posts be steadied by heaping about them, earth or stones. 
Next, with the assistance of a spirit-level, let each post be 
sawed off, so as to bring their tops to the same horizontal 

12 


178 


ELEMENTS OF SURVEYING. [BOOK IV 


plane, and by means of the theodolite, let a line be marked 
on the top of each post, in the direction of the base. 
This line will determine the direction in which the rods 
are to be placed, and the contact of the ends must all be 
on this line. 

The contact of the rods should be made with' great care, 
so as to avoid moving the rod already established; and 
this will be more readily done, when three rods are used. 
The measurement should be repeated two or three times 
to guard against error. 

14. If the nature of the ground does not admit of the 
posts being brought to a level, let them, by means of the 
theodolite, be brought into an oblique plane AB, and aftei 


B 



having measured, as before, the line AB, determine accu¬ 
rately the difference of level between the points A and B , 
equal to BC: then, from the right-angled triangle ABC. we 
should find the horizontal distance AC = VAif — BC'. 

15. In very extensive surveys, the base should be several 
miles in length, and the apparatus for measurement, as well 
as the operations on the field, become more complicated. 
For a full description of a very perfect base apparatus, and 
the method of using it, the reader is referred to Prof. 
B ache’s pamphlet, on the subject—the details of the descrip¬ 
tion would exceed our limits. 

TRIANGULATION. 

16. The theodolite is generally used for measuring the 
angles of a trigonometric survey. The extent of the survey, 
and the standard of accuracy to which the results are re¬ 
quired to conform, must determine the size and perfection 
of the instrument to be employed. The angles of the pri¬ 
mary triangles of the United States Coast Survey, are meas¬ 
ured with theodolites, whose horizontal circles are 24 or 80 
















SEC. I.j 


TRIANGULA TION 


179 


inches in diameter 5 and to eliminate as much as possible, 
every source of error, great numbers of operations are made 
on each station, the reading's being made on different points 
of the arc. Usually from 40 to 60 observations are made 
for each angle—one measurement, with the telescope direct 
and one with it reverted, constituting a complete observa 
tion. With these precautions, it has been found that the 
error in a primary triangle (wt ere the sum of its three an¬ 
gles has been compared with 180°), has fallen much with¬ 
in 8 seconds. The error of 8 seconds has been adopted as 
the highest admissible limit of error. 

17. Observations are also made at the principal stations 
upon the pole-star, and other stars near the pole, for the 
purpose of determining the angle, made by the sides of the 
triangle with the meridian. In minor surveys, and in a 
secondary triangulation, the operations are much less elabo¬ 
rate ; still, every precaution is to be taken to insure the 
greatest attainable accuracy. As a general rule, all the an¬ 
gles of every triangle, should be measured, if possible. 

18. To illustrate the manner of carrying on a minor 
triangulation, let us refer to the plan of the harbor [plate 
6], in which AB is the measured base, (7, Z), A, &c., tri¬ 
angulation points, at which signals have been erected. 
Commence the triangulation at A , the west end of the 
base; and for convenience in plotting, it would be well 
to make the line, passing through the 0 point, and 180° 
parallel, in each position of the instrument, to the base 
AB. Having brought the 0 of the vernier to the 0 of the 
limb, clamp the vernier plate, and direct the upper teles¬ 
cope to the signal at J5, and clamp the limb. Enter the 
observation as in the following table: 

OBSERVATION AT STATION A. 


Name of Station. 

Vernier I. 

Vernier II. 

Mean. 

Station B 

o 

o 

o 

o 

o 

o 

o 

O 

o 

o 

o 

00° 00' 00" 

Station E 

72° 24' 55" 

2 5' 5" 

72° 25' 00' 

Station Gr 

138° 34' 56'' 

35’ 4" 

138° 35' 00' 

&c. 

&c. 

&c. 

&c. 


















180 


ELEMENTS OF SURVEYING. [BOOK IV 


Having recorded the reading of the first vernier, and 
the minutes and seconds of the second vernier, unclamp 
the vernier plate, and direct the telescope to the station at 
E, and record both verniers, as before. Again unclamp the 
vernier plate, and direct the telescope on the signal at G ; 
and then read and record, as before. 

Having determined the angles subtended by all the 
signals visible from A, let the theodolite be removed to 
B. Bring the 0 of the vernier I to 180° on the limb, and 
direct the telescope on the signal at A—the line (0°, 180°) 
will then be parallel to its first position, and the limb may 
be clamped. Bead now the angles to the signals at A, E\ 
0\ &c., and record as before. 

If the theodolite is now removed to the station E, the 
line (0°, 180°), may be made parallel to its first position, 
by adding 180° to the reading of the first vernier, from A 
to E , and then directing the telescope on the signal at A . 
The line (0°, 180°), will thus be made parallel to AB, and 
the reading may be made and recorded as before; and 
so on until all the stations have been visited, and the an¬ 
gles measured. From the field records, the angles BAE\ 
EAG , ABE\ EBG ) &c., may be easily deduced, the whole 
may be plotted on paper, or the several sides may be com¬ 
puted trigonometrically. It may be observed that the line 
(0°, 180°), has been made parallel to the base line at each 
station; where great accuracy is required, this cannot be 
done, since a single reading is insufficient to give the angle. 
The angle is then determined, as directed in the previous 
article, or by means of the principle of repetition. 

19. To illustrate this principle of repetition, suppose the 
0 of the vernier to coincide with the 0 of the limb, and the 
telescope to be directed, from the station A, upon one of the 
objects, as the signal at B. Clamp the limb, and unclamp¬ 
ing the vernier plate, direct the telescope on the second ob 
ject, as the signal at E. If we now clamp the vernier 
plate, and unclamping the limb, direct the telescope on the 
signal at B, the line (0 r , 180°), of the limb, will make 
with AB , an angle equal to BAE. Again clamp the limb, 


SEC. I.] TRIANGULATION. 181 

and unclamping the vernier plate, direct the telescope on 
the signal at E. The reading will evidently be equal to 
twice the angle BAE, and if we repeat the operation, the 
reading will be three times the angle, and so on. After 
ten repetitions, if we add 360° each time the 0 of the 
vernier passes the 0 of the limb, the final reading will be 
ten times the angle BAE\ affected with the joint errors o! 
the ten observations, and one-tenth of this will be the read¬ 
ing required, to a greater degree of accuracy than could 
probably be attained by a single observation. 

20. The method of reading angles, by this mode, is a i 
follows: 

Angles at station A, between signals B (left), and E 
(right.) 

June 8th , 1851. 


No. oi' Repe¬ 
titions. 

Vernier I. 

Vernier 

II. 

Mean of Verniers. 

*• 

1 

72° 24' 55" 

25' 5" 

72° 25' 00" 


2 

144° 49' 55" 

50' 0" 

144° 49' 58" 


3 

217° 14' 50" 

15' 10" 

217° 15' 00" 


4 

289° 39' 50" 

© 

o 

© 

289° 39' 55" 

4)289 39'55" 


• 


Mean reading 

72° 24' 59" 


FILLING UP THE SURVEY. 

21. After the triangulation is completed, the interior 
may be filled up by the aid of the Compass, or the plane- 
table. 

USE OF THE COMPASS. 

22. When the secondary and tertiary triangles have been 
considerably multiplied, the compass is taken in hand. 
The field-notes may be kept in the following manner. Di¬ 
vide a page of the note-book into two equal parts, by two 
parallel lines near to each other, and consider each part as 
a separate leaf or page. Each leaf is divided mtc three 


















182 


ELEMENTS OF SURVEYING. [BOOK IV 


spaces, i.nd the middle space is generally smaller than either 
of the others, which are equal. 

The notes begin at the bottom of the first page, and 
run up the page to the top. They then commence again 
at the bottom of the next page, and run up to the top; 
thence to the bottom of the third page, and thus, for as 
many pages as the work may require. 

When the compass is used in the way we are about to 
explain, the distances to objects which lie on the right or 
left of the courses, are determined by means of offsets. 

The beginning of every course is designated in the mid¬ 
dle column by 0, and the bearing is entered directly above. 
The other figures of the middle column, express the dis¬ 
tances from the beginning of each course to the offsets, and 
those in the side columns indicate the lengths of the offsets, 
or the distances to objects on the right or left of the com¬ 
pass lines. 

To explain more definitely the manner of using the 
compass on the field, let us suppose that we have deter¬ 
mined the prominent points and longer lines with the 
theodolite. Place the compass at A (Plate 6), and take the 
bearing of the line AE\ which is S 12° W. 































SEC. I.] 


THE PLANE-TABLE. 


183 


AE any distance as Aa equal to 130 yards, and make an 
offset to the lake, which we measure and find to be 50 
yards. Enter the 130 in the middle column, and as the 
lake lies on the right (in going from A to E), we insert 
the 50 in the right hand column. 

We then measure along the line AE to b, 350 yards 
from A. Here we make a second offset to the lake, and 
find it to be equal to 100 yards. Having entered the dis¬ 
tances in the notes, we measure to q, the point where the line 
AE crosses the creek, and we enter the distance from A, 
415 yards. 

At d, we lay off an offset on the left, to the pond, 70 
yards: at e, an offset to the mouth of the creek, 150 yards: 
and at E, where the course terminates, an offset to the 
lake, of 160 yards. The entire distance from A to A is 
800 yards. 

At E\ we take the bearing to II, which is N 50° E. 
Having measured along this line to f 315 yards, we make 
an offset to the pond, on the left, of 50 yards, and to the 
shore, on the right, of 90 yards. Having entered these 
distances, we recommence the notes at 315 below, which we 
suppose to be at the bottom of the second page. Having 
reached H, the extremit} r of the course, we enter the en¬ 
tire distance from E, 680 yards. We next take the bear¬ 
ing to i, S 52° E. We then measure the distances to m, 
n, p, and I, and enter them, together with the offsets, as 
in the notes. 

23. It is also well to make, in the columns on the right 
and left, such sketches of the ground, fields, houses, creeks 
and rivers, as will afford the means of making an accu¬ 
rate delineation on paper. 

THE PLANE-TABLE—ITS USES. 

24. PI. 3, Fig. 1. The plane-table consists of two parts; 
a rectangular board CDBA , and a tripod EIIG , to which 
it is firmly secured. 

Directly under the rectangular board are four milled 
screws which pass through sockets inserted in a horizontal 


184 


ELEMENTS OF PURVEYING. [BOOR IV 


brass plate : these screws are worked against a second ho¬ 
rizontal plate, for the purpose ot levelling the table; the 
table having a ball and socket motion, similar to the limb 
of the theodolite. 

For the purpose of levelling the table, a small detached 
spirit-level is used. This level being placed over the 
centre, and also over two of the levelling screws, the screws 
are turned contrary ways until the level is horizontal; 
after which, it is placed over the other two screws, and 
made horizontal in the same manner. 

Between the upper horizontal plate and the table, there 
is a clamp-screw, similar to the clamp-screw of the theodo¬ 
lite, which being loosened, the table can be turned freely 
about its axis. There is, also, a small tangent-screw, by 
which the smaller motions of the table are regulated, after 
the clamp-screw is made fast. Neither of these screws can 
be seen in the figure. 

The upper side of the table is bordered by four brass 
plates, about one inch in width, and the centre of the table 
is marked bjr a small pin, F. About this centre, and tan¬ 
gent to the sides of the table, conceive a circle to be de¬ 
scribed. Suppose the circumference of the circle to be di¬ 
vided into degrees and parts of a degree, and radii to be 
drawn through the centre and the ]3oints of division. The 
points in which these radii intersect the outer edge of the 
brass border, are marked by lines on the brass plates, and 
the degrees are numbered in the direction from left to 
right, from the point L to the point 7J 180°, and from the 
point I to the point A, 180°. In some plane-tables, how¬ 
ever, they are numbered from 0 to 360°. 

There are, generally, diagonal scales of equal parts cut 
on the plates DLG and AJL\ the use of which will be ex¬ 
plained hereafter. 

Near the two other edges of the table, two small grooves 
are made, into which the plates of brass DB and CA are 
fitted, and these plates are drawn to their places by means 
of milled screws, which pass through the table from the 
under side, and screw firmly into the plates. The heads 


% 


SEC. I.] 


THE PLANE-TABLE. 


185 


of two of the screws, Q and S, are seen in the figure, as 
also one of the plates and its two screws in Fig. 3. The 
object of these plates is to confine a sheet of paper on the 
table. By loosening the screws, and pressing them up¬ 
wards, the plates are raised above the surface of the table; 
the edges of the paper can then be placed under them: 
then, by turning the screws back again, the plates are 
drawn down and the paper held tightly. Fig. 1 represents 
the table with the paper partly put upon it: one edge of 
the paper has been placed under the plate DB, and the 
screws 8 and (), tightened. The paper, before being put 
on, should be moistened, in order to expand it; and then, 
after it has been dried, it will fit closely to the table. 

A ruler, AB (Fig. 2), with open vertical sights, is used 
with the plane-table. This ruler has a fiducial edge, which 
is in the same vertical plane with the hairs of the sights. 
A ruler with a telescope, and a vertical limb, similar to the 
vertical limb of the theodolite, is sometimes used with the 
plane-table. A compass, also, is often attached to the table, 
to show the bearings of the lines. 

The plane-table is used for two distinct objects. 

1st. For the measurement of horizontal angles. 

2dly. For the determination of the shorter lines of a 
survey, both in extent and position. 

TO MEASURE A HORIZONTAL ANGLE. 

25. Place, by means of a plumb, the centre of the table 
directly over the angular point: then level the table; after 
which, place the fiducial edge of the ruler against the small 
pin at the centre : direct the sights to one of the objects, 
and note the degrees on the brass plate ; then turn the 
ruler and sights to the other object, and note the degrees 
as before. If the ruler has not passed over the 0 point, 
the difference of the readings io the angle sought; but, if 
it has, the larger taken from 180°, and the remainder added 
to the smaller, gives the required angle. 

TO DETERMINE LINES IN EXTENT AND POSITION. 

26. Having placed a paper on the table, examine the 


186 


ELEMENTS OF SURVEYING. [BOOK IV 


objects and lines which are to be determined, and select 
for a base a convenient portion of such a line of those 
already formed in the triangulation, that most of the ob¬ 
jects can be seen from its extremities. Then place the 
plane-table with its centre, nearly, though not accurately 
over one extremity of the base; make it truly horizontal," 
and turn it until the larger part of the paper lies on the 
same side of the base with the.objects. 

Then, tighten the clamp-screw, and mark with a pin the 
point of the paper directly over the station, which point is 
determined most accurately by suspending a plumb from 
the lower side of the table. Press the pin firmly on this 
point, bring the fiducial edge of the ruler against it, and 
sight to the other extremity of the base line, and mark 
with the pin or pencil, the direction of the line on the 
paper. Sight in like manner to every other object, and 
draw on the paper the corresponding lines, numbering them 
from the base line, 1 , 2 , 3, 4, &c. 

Then, with a pair of dividers, take from the scale a 
certain number of equal parts to represent the base, and 
lay off the distance on the base line from the place of the 
pin. Take up the table, carry it to the other extremity 
of the base, and place the point of the paper correspond¬ 
ing to that extremity, directly over it. Place the fiducial 
edge of the ruler on the base line, and turn the table, by 
means of the tangent-screw, until the sights are directed to 
the first station. If, however, in bringing the table to this 
position, the corresponding point of the paper has been 
moved from over the extremity of the base line, move the 
legs of the tripod until it is brought back to its place. 
Let the table be then levelled, after which, place the ruler 
again on the base line, and bring the table to its proper 
position by the tangent-screw, and continue the adjustment 
until the extremity of the base line on the paper is directly 
over the station, and in the same vertical plane with the 
base line on the ground. Then direct the sights to all the 
objects sighted to from the other station, and mark the 
lines 1 , 2 , 3, 4, &c., from the base line, as before. The 
intersections of the corresponding lines 1,1, 2 , 2 , 3,3, 4,4, 


SEC. I.] 


THE PL AXE TABLE 


187 


"&c., determine, on the paper, the positions of the several 
objects; and a reference of these lines to the scale of equal 
parts, determines the true distances. 



27. Let it be required, for 
example, to determine, by 
means of the plane-table, the 
relative positions of several 
houses. 

From station A, and on 
one of the lines of the tri¬ 
angulation, as AB, measure 
the base line AN, which we will suppose equal to 800 
yards. Place the plain-table at A, and sight to the corners 
of the houses, and mark the lines 1, 2, 8, 4, &c. Then 
remove the table to N, and sight to the same corners as be¬ 
fore, and draw the lines as in the figure. The points at 
which they intersect the corresponding lines before drawn, 
determine the corners of the houses. The front lines of 
the houses may then be drawn on the paper. Draw lines 
at right angles to the front lines, and on them lay off the 
depths of the houses, with the same scale as that used for 
the base line. 


To find the length of any line drawn on the paper, as 
the line 1, drawn through A, for example, place the divi¬ 
ders at A and extend them to the other extremity of the 
line, and then apply the line to the scale. The length of 
the line 1 is equal to 198 yards. 


28. In this example, we de¬ 
termine from the base line 
CD, the positions of the points 
F, E, and H. 



OF CHANGING THE PAPER. 

29. When one paper :s filled, and there is yet more 
work to be done, let the paper be removed, and a second 
paper put on the table; after which, the table may be 
used us before. 








188 


ELEMENTS OF SURVEYING. [BOOK I 


Now, in order that the two papers may be put toge¬ 
ther and form one entire plan, it is necessary that two 
points determined on the first paper, oe also determined 
on the second; and then, by placing the lines joining 
these points, one on the other, all the lines on the f wo 
papers will have the same relative position as the corres¬ 
ponding lines on the ground; and the same for as many 
papers as it may be necessary to use. If different scales 
are used, the corresponding points will not join, and then 
the work must be reduced to the same scale before the 
papers can be put together. 

In the first example, the position of the point F was de¬ 
termined, in order to unite the first paper with the second. 

In tiie second example, we sighted from G and D, the 
extremities of the base line, to the points N and F\ we 
thus determined the line NF on the second paper. Pla¬ 
cing the line NF of the one paper on NF of the other, we 
have the following plan. 



In this plan, all the points and lines are accurately laid 
down. Any number of papers may be joined in the same 
manner. 

ft 

80. The principal use of the plane-table is for the in¬ 
terior filling up of trigonometrical surveys; it is also used 
with advantage, when only a plot of a field is wanted. 

It ought not be used for the determination of long lines, 
nor can it be relied on for determining extended areas. 

Having finished the field-work, some corrections are ne¬ 
cessary, before plotting the survey. The principal correc¬ 
tions are, the reduction to the centre of the station, &vxl 
the correction for spherical excess. 




SEC. I] 


CORRECTIONS. 


189 


REDUCTION TO THE CENTRE. 


81. It sometimes happens that fixed objects, as steeples, 
towers, and the like, are used instead of signals, in a sur¬ 
vey. The theodolite cannot be placed over the centre of 
such stations. In all such cases, the instrument must be 
planted as near as possible to the station; then the angles, 
subtended by the various objects being measured, the true 
angle subtended at the centre of the station, is computed 
by the following formula. 

Suppose A, B and C , to be 
the three stations. Let us sup¬ 
pose that the theodolite cannot 
be placed over C, but that it 
can be placed at I), a point 
near C. 

Let the angles ABB and ADC be 
measured; also the distance CD, and 
the distances AC and BC computed, 
approximative^, from the side AB and 
the angles A and B. The true angle 
ACB may then be found. 

For, ABB— ACB 4- CAD (Georn., Bk. I., Prop. 25, C. O'); 
and ABB — ADB + DBC: 

hence, by equating the equal values, 

ACB + CAD = ADB + DBC, 

ACB= ADB A DBC- CAD. 

CD : : sin BDC : sin DBC \ 

CD 

sin DBC = sin BDC : 



o D 


or, 

But 


BC 


or, 


and 


or, 


AC : CD : : 
sin CAD = 


BC 
sin ADC 
CD 


sin CAD\ 


AC 


sin ADC. 


lienee, by substitution, we have 

/ CD CD \ 

ACB = ADB -f sin BD C — sin ADC); 

for, since the distance DC is very small in comparison with 
BC and AC, the angles DBC and CAD are very small; 
and hence, their sines may be substituted for the angles 

fl. 







190 


ELEMENTS OF SURVEYING. 


[BOOK TV 


It is to be observed, that when the radius is unity, in 
the above formula, the natural sines of the angles are used, 
and that the correction within the parenthesis, is expressed 
in linear units, and will be positive or negative, according 
as the second term is less or greater than the first. 

To convert the linear correction into seconds of an arc, 
whose radius is unity, let the deduced correction, within 
the parenthesis, be denoted by c. Then, since the radius 
is 1, we shall have 

length of semi-circumference 
: the linear correction 
: : the number of seconds in 180° 

: the number of seconds in the correction: 
that is, denoting the number of seconds in the correction 
by n, 

3.1416 : c : : 648000" : w; or n = c X 206264.3" : 

c will, in all cases, be a very small fraction. 

This correction is not often necessary, for in extensive 
operations, such stations are chosen as will allow of the 
measurement of all the angles, and in secondary triangles, it 
is admissible to measure only two of the angles. 

SPHERICAL EXCESS. 

32. It has already been noticed, that the triangles meas¬ 
ured, are on the surface of a sphere, and consequently, the 
angles taken between any three points, by a theodolite, are, 
strictly speaking, the angles of a spherical triangle; hence, 
the sum must exceed 180°, (Greom., Bk. IX., P. 14). This ex¬ 
cess is called the spherical excess. In the processes of trian¬ 
gulation, we reduce all triangles to rectilineal triangles; and 
hence, the sides of the triangle, which we seek, are chords 
of the sphere, and not arcs measured on the surface. 

33. In small triangles, where the sides do not exceed 
6 or 8 miles, the spherical excess may be altogether ne¬ 
glected; but in large triangles, it must be taken into ac¬ 
count. Of all the methods, yet known, of correcting for 
the spherical excess, Legendre’s is considered the best 



SEC. I.] 


SPHERICAL EXCESS. 


191 


This method is based upon the proposition that, the area 
of a spherical triangle , ivhich is very small when compared 
with the entire surface of the sphere , is nearly identical with a 
rectilineal triangle , whose sides are of the same length as those 
of the spherical triangle , and whose angles are each diminished 
by one-third of the spherical excess. 

84. The first thing, then, is to find the spherical ex¬ 
cess, and for this, we must know the area of the triangle. 
The rules for determining tne area of the rectilineal trian¬ 
gles, will afford results sufficiently near, and the first ap¬ 
proximate area may be computed in square feet, as though 
the triangle were rectilineal. Having found this area, the 
formula of Legendre, gives the logarithm of the spherical 
excess, estimated in seconds, equal to the logarithm of the 
area of the triangle computed in square feet, minus the 
constant logarithm 9.326770. That is, if we put 

E = the spherical excess, in seconds. 

A = area of the triangle, in square feet. 

Constant log. = 9.326770; 

we shall have, 

Log E — log A — 9.326770. 

Having found the spherical excess, we divide it by 3, 
and then diminish each angle of the triangle by the quo¬ 
tient ; the sum of the three angles should then be equal to 
180°. With these new angles, we compute all the parts of 
the triangle. 

35 . The spherical excess between latitude 25° and 45°, 
is about 1 " for an area of 75.5 miles ; hence, to obtain a 
close approximation to the spherical excess, divide the num¬ 
ber of square miles in the area of the triangle by 75.5, the 
quotient will be the number of seconds required. 

36 To find the sj herical excess, knowing the two sides 
a and h f and the included angle C. 

a b sin C. 

2 R 


area = 



192 


ELEMENTS OF SURVEYING. 


[LOOK IV 


Suppose a = 248230 feet, b = 212628 feet, and C — 103'" 
i9' 10". 

a . 248230 .log_ 5.394854 

b . 212628 .log_ 5.327620 

G. . 103° 19' 10" . . . log sine . . . 9.988158 

ar. comp, of 2, diminished by 10 . . 1.698970 



20.409602 

Log of E.... , 

. ... 10. 

Log A. 

. . . 10.409602 

Constant logarithm . 

. . . 9.326770 

Hence, E=12.V .. 



the three measured angles ought therefore to exceed 180°, 
by this amount. The angles being corrected, by subtract¬ 
ing 4.J" from each, the jrarts of the triangle may be com¬ 
puted, by regarding the sides as rectilineal. 

PLOTTING THE TRIANGULATION. 

37. The sides of the triangles being computed, after 
having made the necessary corrections, the work may then 
be plotted, as already explained, either by means of the 
circular protractor, or by the method of chords. 

THE CIRCULAR PROTRACTOR. 

38. This instrument consists of a brass circular limb 
(PI. 2, Fig. 4), of about six inches in diameter, with a 
movable index AB ) having a vernier at one extremity A , 
and a milled screw at the other extremity B , with a con¬ 
cealed cog-wheel that works with the cogs of the limb, and 
thus moves the index AB about the centre of the pro¬ 
tractor. At the centre of the protractor is a small circular 
glass plate, on which two lines are cut; the point of their 
intersection, is the exact centre of the instrument. The 
limb is generally divided to half degrees; the degrees are 
numbered from 0 to 360. 

At the 0 point, and at the opposite extremities of the 
diameter passing through that point, are small lines on the 
inner edge ol the limb ;• the two extremities of the diam- 












SEC. L] 


OF PLOTTING. 


193 


eter, perpendicular to tliis latter, are designated in tlie same 
way. 

Two angular pieces of brass, each haying a small and 
sharp steel pin at its extremity, are fastened to the index, 
and revolve freely around the lines ab and cd. The small 
screws, a, b, c, and d, move them in the directions of the 
lines ab, cd, for the purpose of bringing the steel pins ex¬ 
actly into the line which passes through the 0 of the in¬ 
dex and the centre of the protractor. 

To adjust them to their places, place the centre of the 
protractor over a marked point, and the 0 of the index to 
the 0 of the limb. Then mark the place of the index by 
the pins: after which, turn the index 180°, and see if the 
pins will mark the same points as before. If they do, the 
index is adjusted; if they do not, correct the error with the 
screws a, b, c, and d. 

T0 LAY ©FF AN ANGLE WITH THE PROTRACTOR. 

39. Let its centre be placed over the angular point, and 
the diameter passing through 0 and 180°, on the given line. 
Turn the screw that works the index, until the 0 of the 
vernier coincides with the division corresponding to the 
given angle; then let the angular brass pieces be turned 
down; the points dotted by the steel pins will show the 
direction of the required line. 

If this line does not pass through the angular point, 
the pins are out of place, and must be adjusted. 

FIRST METHOD OF PLOTTING. 

40. Suppose it were required to make the plan of the 
harbor on a scale of 450 yards to an inch. 

Divide the. length of the base line AB, which we will 
suppose equal to 1140 yards, by 450, and the quotient 2.53 
will express the length which is to represent the base line 
on the paper (Bk. I., Art. 54.) 

Draw an indefinite line AB, to represent the base, and 
having chosen any point, as A, for the first station, lay off 
2.53 inches to B. The other extremity of the base line 
will thus be determined. 

13 


194 


ELEMENTS OF SURVEYING. [BOOK IV. 


Then, place the circular protractor at A, and lay off 
the angle BAE, and then the angle EAG. Next, place 
the protractor at B, and lay off the angles A BE and EBC . 
The intersection of the .ines AE and BE will determine 
the station E. Let the protractor be then placed at this 
point, and all the angles of station E\ laid down. 

The point G, where EG intersects AG, and the point 
C, where EC intersects BC, will then be found. 

By placing the protractor at C and G, we can deter¬ 
mine the points D and F, when the place, on the paper, of 
all the stations will be known. 

To unite the work done with the compass, spread the 
compass-notes before you, and draw through A a line to 
represent the meridian. This line makes an angle of 12° 
with the course AE. 

Then, lay off from the scale the distances A a, Ab, Aq, 
At, Ad, Ae, and at the several points erect perpendiculars 
to AE. Lay off on these perpendiculars the lengths of the 
offsets, and the curve traced through the points so deter¬ 
mined, will be the margin of the lake. 

At E, draw a parallel to the meridian through A, and 
lay down the course EH, which makes an angle of 50° with 
the meridian. Then, lay down the several distances to the 
offsets, and draw the offsets and lav off their lengths. Do 
the same for the course HI, and all the compass-work will 
be plotted. 

The work done with the plane-table (Art. 28), is united 
to the work done with the theodolite, by simply placing 
the line AN on the paper of the plain-table, upon the line 
AN, drawn on the plot of the triangulation. 

SECOND METHOD OF PLOTTING. 

41. Place the centre of the protractor near the centre 
of the paper, and draw a line through the points 0 and 
180°. This line will have the same position with the cir¬ 
cular protractor that the base line AB had with the limb 
of the theodolite. 


8 EC. T.J 


METHOD OF CHORDS. 


195 


Lay off then from the 0 point an arc equal to the direc¬ 
tion from A to E, also a:i arc equal to the direction A 0, 
and through the centre point, and the points so determined, 
draw lines. Lay off in succession, in a similar manner, 
the directions taken at all the stations; and through the 
centre point, and the points so determined, draw lines, and 
designate each by the letters of the direction to which it 
corresponds. 

Now, since all the lines drawn on the paper have the same 
position with the circular protractor, as the corresponding 
lines on the ground have with the limb of the theodolite, 
it follows that each direction will be parallel to its corres¬ 
ponding line upon the ground. 

Hence, any line may be drawn parallel to that passing 
through 0 and 180°, to represent the base line AB. Having 
drawn such a line, and marked a point for the station A , 
lay off the length of the base, and the extremity will be 
the station B. 

Through A' and B, so determined, draw parallels re¬ 
spectively to the lines corresponding to the directions AE 
and BE\ and the point of intersection will determine station 
E. Through B and E draw parallels to the lines which 
correspond to the directions BO\ CE, and their point of 
intersection will determine station C. Through C and E 
draw lines parallel to the lines corresponding to the direc¬ 
tions CE and ED , and the point of intersection will de¬ 
termine I). In a similar manner we may determine the 
stations F and G. 


METHOD OF CHORDS. 


42. Let us first prove that the cl Lord of a given arc u 
equal to the sine of half the arc with double the radius. 


Let DAE be any given angle, 
and ATI a line bisecting it. Let 
DC be the chord of the arc CD, 
described with a given radius, 
and HF parallel to CD, the sine 
of half the given angle, to a radius 






196 


ELEMENTS OF SURVEYING. [BOOK IV 


Since AF—2AC we have, from similar triangles, EF 
2KC, but DC=2KC\ hence EF— CD. 


TO LAY OFF AN ANGLE. 


43. To avoid, as far as possible, 
the use of fractions, let us suppose 
the radius of the table of natural 
sines to be 1 ten , or 10 inches. 

Take from a scale 5 equal parts, 
with which as a radius, from the centre A, describe an 
arc CD. Take from the table the natural sine of half 
the arc, and remove the decimal point one place to the 
right; the result will express the sine of half the arc to the 
radius 10, or the chord of the arc to the radius 5. From 
the same scale, take this sine in the dividers, and from" C, 
as a centre, describe an arc cutting CD in D\ draw AD , 
and CAD will be the angle required. 



90 ° 


This is the most accurate of all the methods of laying 
off an angle, and it may also be applied advantageously to 
the second method of plotting, thus: 

Draw a fine straight line, generally 
in the direction of the meridian or of 
the base line of the survey; and also 
a line exactly perpendicular to it. From 
the point of intersection, as a centre, 
with a radius of 5 equal parts of the 
scale, describe the circumference of a 
circle cutting the straight lines in the points marked 0 
and 90°. 



To lay off an angle, as for instance, the angle 14° 29‘. 
The half of it is 7° 14' 80", the natural sine of which is 
0.126005, or 1.26 to the radius of 10 inches. Set off from 
0 to 5, as in the figure, this distance taken from the scale, 
and through the two points 5, 5, thus determined, draw a 
straight line. This line should pass through the centre, 
and will make with the line (0, 0) the angle 14° 29'; and 
any line on the paper drawn parallel to it, will make with 
the line (0, 0) the same angle. The further application is 
obvious. 







SEC. II.] 


MARITIME SURVEYING. 


197 


SECTION II. 

MARITIME SURVE I r ING. 

44. When, in connection with a trigonometrical survey 
on shore, a harbor is to be surveyed for the purpose of 
ascertaining the channels, their depth and width, the posi¬ 
tions of shoals, and the depth of water thereon, other 
means must be used, and other examinations made in ad¬ 
dition to those already referred to. 

Let buoys be anchored on the principal shoals and along 
the edges of the channel, and using any one of the lines 
already determined as a base, let the angles subtended by 
lines drawn from its extremities, to the buoys respectively, 
be measured with the theodolite. Then, there will be 
known in each triangle the base and angles at the base, 
from which the distances to the buoys are easily found ; 
and hence, their positions become known. 

Having; made the soundings, and ascertained the exact 
depth of the water at each of the buoys, several points of 
the harbor are established, at which the precise depth of 
the water is known ; and by increasing the number of the 
buoys, the depth of the water can be found at as many 
points as may be deemed necessary. 

45. If a person with a theodolite, or with any other in¬ 
strument adapted to the measurement of horizontal angles, 
be stationed at each extremity of the base line, it will not 
be necessary to establish buoys. A boat, provided with 
an anchor, a sounding line, and a signal flag,»has only to 
throw its anchor, hoist its signal flag, arid make the sound¬ 
ing, while the persons at the extremities of the base line 
measure the angles;—from these data, the precise place oi 
the boat can be determined. 

46. There is another method of determining the places 
at which the soundings are made, tl.at admits ot great 


198 ELEMENTS OF SURVEYING. [BOOK IV 

despatch, and which, if the observations are made with 
care, affords results sufficiently accurate. 

H aving established, trigonometrically, three points which 
can be seen from all parts of the harbor, and having pro 
vided a sextant, let the sounding be made at any place in 
the harbor, and at the same time the three angles subtend¬ 
ed by lines drawn to the three fixed points, measured with 
the sextant. 

The problem, to find, from these data, the place of the 
boat at the time of the sounding, is the same as example 
6, page 62. 

It is only necessary to measure two of the angles, but 
it is safest to measure the third also, as it affords a veri¬ 
fication of the work. 

The great rapidity with which angles can be measured 
with the sextant, by one skilled in its use, renders this a 
most expeditious method of sounding and surveying a 
harbor. 

The sextant is not described, nor are its uses explained 
in these Elements, because its construction combines many 
philosophical principles, with which the Surveyor cannot 
be supposed conversant. 

47. There is yet another method of finding the sound¬ 
ings, which, although not as accurate as those already ex¬ 
plained, will, nevertheless, afford results approximating 
nearly to the truth. It is this:—Let a boat be rowed uni¬ 
formly across the harbor, from one extremity to the other 
of any of the lines determined trigonometrically. Let 
soundings be made continually, and let the precise time o^ 
making each be carefully noted. Then, knowing the 
length of the entire line, the time spent in passing over it, 
as also the time of making each of the soundings, we can 
easily find the points of the line at which the several 
soundings were made; and hence, the depth of water at 
those points becoir.es known. 

48. If a person stationed on shore with a theodolite, takes 
the bearing of the boat, at every second or third sounding, 
determined by hoisting a flag, it will fix the positions of the 


SEC. II.] 


MARITIME SURVEYING. 


199 


soundings with great accuracy. Soundings may thus be 
made along any number of known lines, and a comparison 
of the depths found on different lines, at or near their 
points of intersection, will show with what degree of ac¬ 
curacy the work has been done. 

Sounding-lines should be made of strong cord, and di¬ 
vided into feet or fathoms, by different colored rags or 
other marks. The lead is shaped like 
the frustum of a cone, with the base 

hollowed out, to hold some grease. 

The land or mud of the bottom adheres 
to the grease, and thus shows the na¬ 
ture of the bottom, which should be en¬ 
tered in the field-book, and laid down 
upon the map. As the cord is liable 
to change its length, it should be com¬ 
pared from time to time with some 
standard. In tide-waters, the exact time 
of each sounding is to be noticed, and 
an assistant should note the height of the tide at regular in¬ 
tervals, upon a tide-guage. The tide-guage is permanently 
placed at some convenient point of the harbor, and its 0 
point is referred by means of a spirit-level, to some fixed 
bench-mark, on a level with mean low-water mark, to 
which all the soundings must be reduced. 

49. Having plotted the work done with the theodolite, 
as also the outline of the harbor traced with the compass, 
it remains to delineate the bottom of the harbor; and this 
is done by means of horizontal curves, which have already 
been used to represent broken or undulating ground. 

Let the plane of reference be taken through low-water 
mark, or to coincide with the surface of the water at low 
tide. The accuracy with which the bottom of the harbor 
is to be delineated, will guide us in fixing the distance be¬ 
tween the horizontal planes of section. 

The , first horizontal plane should be passed at a dis¬ 
tance below the shallowest point that has been sounded, 
equal to the number of feet fixed upon for the distance 
between the planes of section; and the curve, in which it 



200 


ELEMENTS OF SURVEYING 


[BOOK IV 


intersects tlie bottom of the harbor determined as in Book 
III. Sec. II. And similarly, for the other horizontal planes 
of section. 

Having thus delineated the bottom of the harbor, and 
noted on the map the distance of each intersecting plane 
below the plane of reference, let such lines be drawn ay 
will indicate the channels, shoals, sunken rocks, and direc 
tion of the current. 

In the example given in plate 6, soundings have been 
made in three directions from the sand-bar in the harbor, 
and also from the rocky shore across to the light-house. 




* L t 


BOOK y. 

OF NAVIGATION. 


SECTION I. 

DEFINITIONS. 

1. We have given, in tlie preceding parts of this work, 
various applications of Plane Trigonometry. We propose, 
in this Book to explain the best methods of determining 
the place of a ship at sea. This application of Trigonom¬ 
etry constitutes the science and art of Navigation. 

2. There are two methods of determining the place of 
a ship at sea. 

1st. When a ship departs on her voyage, if we note 
her courses and the distance sailed, we may, at any time, 
by means of Plane Trigonometry, determine her place, very 
nearly. 

2d. By means of observations on the heavenly bodies, 
and the aid of Spherical Trigonometry, we may determine 
with great accuracy, the place of the ship. This method 
is called Nautical Astronomy. 

The first part of Navigation, viz., the cases which can 
be solved without the aid of observations on the heavenly 
bodies, will be alone treated of. 

3. The earth is nearly spherical. For the purposes of 
Navigation it may be considered as perfectly so. It re¬ 
volves round one of its diameters, called the axis, in about 
twenty-four hours. 

4. The great circle, whose poles are the extremities of 
the axis, is called the equator. The poles of the equator 



202 ELEMENTS OF SURVEYING. [BOOK V 

are called the poles of the earth—one is called the north 
pole, and the other the south pole. 

5. The circumference of every great circle which passes 
through the poles, cuts the equator at right angles, and is 
a meridian circle. Every place on the surface of the earth 
has its own meridian ; but for the purposes of Geography 
and Navigation, all the meridians are reckoned from a par¬ 
ticular meridian, which is called the first meridian. The 
English have fixed on the meridian of the Greenwich Ob- 
servatory, for the first meridian. 

6. The longitude of any place is the arc of the equator, 
intercepted between the meridian of that place and the first 
meridian, and is east or west, according as the place lies 
east or west of the first meridian. 

7. The difference of longitude of two places is the arc of 
the equator included between their meridians; this arc is 
equal to the difference of longitudes when they are of the 
same name, and to the sum of the longitudes, when they 
are of different names. 

8. The latitude of a place is its distance from the equator, 
measured on the meridian of the place, and is north or south 
according as the place lies north or south of the equator. 

9. The small circles drawn parallel to the equator, are 
called parallels of latitude. The arc of any meridian inter¬ 
cepted between the parallels passing through any two 
plae.es, measures the difference of latitude of those places; 
this difference is found by subtracting the less latitude from 
the greater, when the latitudes are of the same name, and 
by adding them when they are of different names. 

10. The sensible horizon of any place is an imaginary 
plane, supposed to touch the earth at that place, and to be 
extended indefinitely. 

A plane passing through the centre of the earth, and 
parallel to the sensible horizon, is called the rationed horizon. 

The north and south line, is the intersection of the 
plane of the meridian circle with the sensible horizon, and 
the line which is drawn perpendicular to this, is called the 
east and west line. 


SEC. L] 


NAVIGATION. 


203 


11. The course of a ship, at any point, is the angle which 
her track or keel makes with the meridian. So long as the 
course is unchanged, the ship would sail in a straight line, 
if the meridians were truly parallel; but as the meridians 
bend constantly toward the pole, the direction of her path is 
continually changing, and she moves in a curve called the 
rhumb line. The course of a ship is indicated by the mari¬ 
ner’s compass. 

12. The marin¬ 
er s compass consists 
of a circular card, 
whose circumfer¬ 
ence is divided into 
thirty-two equal 
parts called points ; 
each point being 
subdivided into four 
parts, called quar¬ 
ter points . 

To the under 
side of this card a 
slender bar of mag¬ 
netized steel, called 
a needle , is permanently attached. The direction of the 
needle corresponds to the diameter NS. The diameter EW, 
at right angles to NS, is intended to indicate the east and 
west points. The points of the compass are thus read: be¬ 
ginning at the north point, and going east, we say, north 
and by east , north north east, north east and by north, 
north east; and so on, round the compass, as indicated by 
the letters. 



The card being permitted to turn freely on the pin, on 
which it is poised, as a centre, the line NS will always 
indicate the true magnetic meridian, but this, as we have 
seen in (Bk. II., Sec. 7-14), is not the true meridian, and 
hence, the variation must always be allowed for. 


On the interior of the compass box, in which the card 
swings, are two marks a and Z>, which lie in a line passing 
through the centre ol the card, and the compass box is so 


0 












204 


ELEMENTS OF SURVEYING. 


[BOOK V. 


placed that this line shall be parallel to the keel of the 
ship. Consequently, if b be placed towards the bow of the 
vessel, the point which it marks on the card will show the 
compass course, for the line NS is always on the magnetic 
meridian, and BW is east and west. The course is gene¬ 
rally read to quarter points, and as a quadrant contains 
eight points, each point is equal to 90° -f- 8 = 11° 15'; and 
a quarter point = 11° 15'-r-4=2 J 48' 45V The table of 
Rhumbs, after the Traverse Table, shows the degrees in 
each course, to quarter points. 

13. A ship’s rate of sailing is determined by means of 
an instrument, called the log, and an attached line called 
the log line. The log is a piece of wood in the form of a 
sector of a circle, the rim of which is loaded with lead, so 
that when it is heaved into the sea it assumes a vertical 
position. The log line is so attached as to hold the log 
square against the water, that it may not be drawn along 
after the ship as the line unwinds from the reel, by the 
ship’s forward motion. 

The time in which the log line unwinds from the reel, 
is noted by a sand-glass, through which the sand passes in 
half a minute; that is, in the one hundred and twentieth part 
of an hour . 

For convenience, the log line is divided into equal parts, 
marked by knots , and each part is equal to the one hun¬ 
dred and twentieth part of a nautical or geographical 
mile*. 

Now, since half a minute is the one hundred and twen¬ 
tieth part of an hour, and each knot indicates the one hun¬ 
dred and twentieth part of a mile, it follows that the num¬ 
ber of knots reeled off while the half minute glass runs out, 
will indicate the rate of the ship’s sailing per hour. 


* A geographical mile is one minute, or one-sixtieth of a degree, measured on 
the equator. Taking the diameter-at 7916 English miles, the geographical mil a 
will be about 6079 feet; that is, one-sixth greater than the English mile, which 
is 5280 feet, 




SEC. II.] 


PLANE SAILING. 


205 


SECTION II. 

OF PLANE SAILING. 

14. Let the diagram 
EPQ represent a por¬ 
tion of the earth’s sur¬ 
face, P the pole, and 
EQ the equator. Let 
AB be any rhumb line, 
or track described by 
a ship in sailing from 
A to B . 

Conceive the path of the ship to be divided into very 
small parts, and through the points of division draw meri¬ 
dians, and also the parallels of latitude b'b, c'c, d'd, e'e, and 
B'B : a series of triangles will thus be formed, but so small 
that each may be considered as a plane triangle. 

In these triangles, the sum of the bases 
Ah' + be' + cd' + de' + ef = AB', 

which is equal to the difference of latitude between the 
points A and B. Also, 

b'b + c'c -f- d'd -f- de -f- fB — BB', 

which is equal to the distance that the ship has departed 
from, the meridian AB'P , and is called the departure in 
sailing from A to B. 

Therefore, the distance sailed, the dif¬ 
ference of latitude made, and the departure, 
may be represented by the hypothenuse, 
the base and perpendicular of a right- 
angled triangle, of which the angle op¬ 
posite the departure is the course. 

When ony of the four parts above- 
named are given, the other two can be 
determined. This method of determining 
the place of a ship reduces all the elements to the parts 
of a plane triangle, and hence is called plane sailing. 











\ 


206 ELEMENTS OF SURVEYING. [BOOK V 


EXAMPLES. 


1. A ship from latitude 47° 30' N. Las sailed S. W. b^ 
S. 98 miles. What latitude is she in, and what departure 
has she made ? 


Let C be the place sailed from, CB 
the meridian, and BOA the course, which 
we find from the table of rhumbs to be 
equal to 33° 45'; then AC will be the dis¬ 
tance sailed, equal to 98 miles. Also, A B 
will be the departure, and CB the differ¬ 
ence of latitude. 

Then by the formulas for the solution 
of right angled triangles, 



As radius ar. c. 
: cos C 33° 45' 
: : AC 98 


0.000000 

9.919846 

1.991226 


As radius ar. c. 
: sin C 33° 45' 

: : CA 98 


0.000000 

9.744739 

1.991226 


• CB 81.48 


1.911072 : 


AB 


54.45 


1.735965 


Latitude left 47° 30' 1ST. 

13if. lat. = 81.48 miles = 81.48 minutes = 1° 22' S. 


In latitude 46° OS'. 


Departure, 54.45 miles. 

2. A ship sails 24 hours on a direct course, from lat¬ 
itude 38° 32' N. till she arrives at latitude 36° 56' jST. 
The course is between S. and E. and the rate 51 miles an 
hour. Required the course, distance, and departure. 

Lat. left 38° 32' 1ST. 24 X 5J = 132 miles = distance. 
In lat. 36° 56' 


Diff. 1° 36' = 96 miles. 


As dist. 132 ar. c. 7.879426 As radius ar. c. 0.000000 

: diff. lat. 96 1.982271 : dist. 132 2.120574 

: : radius 10.000000 : : sin course 43° 20' 9.836477 

: cos course 43° 20' 9.861697 : dep. 90.58 1.957051 

~ - — — ■ 



















j-Dy 




: it 

I jSsMl 


* 

A 



Hence, the course is S. 43° 20' E., and the departure 
90.58 miles east. 

?!{■ 

3. A ship sails from latitude 3°, 52' S. to latitude 4° 30' 
N., the course being K W. by W. £W. : required the dist¬ 
ance and departure. 

Ans. Dist. 1065 miles; dep. 939.2 miles TV. 

4. Two points are under the same meridian, one in lat¬ 
itude 52° 30' N., the other in latitude 47° 10' 1ST. A ship 
from the southern place sails due east, at the rate of 9 
miles an hour, and two days after meets a sloop that had 
sailed from the other : required the sloop’s direct course, and 
distance run. 

Ans. Course S. 53° 28' E.; dist. 537.6 miles. 

5. If a ship from latitude 48° 27' S., sail S. W. by TV. 
7 miles an hour, in what time will she reach the parallel 

5f 50° south ? Ans. 23.914 hours. 

* 


SECTION III. 

OF TRAVERSE SAILING. 

15. When a ship, in going from one place to another, 
sails on different courses, it is called Traverse Sailing. The 
determination of the distance and course, from the place of 
departure to the place of termination, is called compounding 
or working the traverse. This is done by the aid of the 
a Traverse Table,” which has already been explained, and 
the method of working the traverse, is in all respects simi¬ 
lar to that adopted in the Prob. of Art. 34, page 123. 

* 


EXAMPLES. 

1. A ship from Cape Clear, in lafc. 51° 25' 1ST., sails, 1st, 
S. S. E. \ E. 16 miles; 2d, E. S. E. 23 miles; 3d. S. W. 
by W. I W. 36 miles; 4th, W. f K 12 miles; 5th, S. E. 
by E. j E. 41 miles : required the distance run, the direct 
course, and the latitude. 




203 


ELEMENTS OF SURVEYING. 


[BOOK V 


We first form the table 
below, in which we enter 
the courses, from the table 
of rhumbs, omitting the 
seconds, and then enter 
the latitudes and depart¬ 
ures, taken from the tra¬ 
verse table, to the nearest 
quarter degree. Thus, in 
taking the latitude and 
departure for 25° 18' we 
take for 25J°. The dif¬ 
ference of latitudes gives 
the line AG, and the dif¬ 
ference of departures the 
line GF. 



TRAVERSE TABLE. 


Courses. 

Dist’s. 

Dili, of Latitude. 

Departure. 

No| 

Amde. 

o 


N. 

s. 

E. 

w. 

1 S. S.E.|E. . . 

00 

r—1 

o 

CM 

16 


1447 

6.83 


2 E. s. E. 

67° 30' 

23 


8.80 

21.25 


3 S. W. by W. i W. 

61° 52' 

36 


17.04 


31.71 

4 W. f 1ST. 

81° 33' 

12 

1.77 



11.87 

5 S. E. by E. i E. . 

59° 03' 

41 


21.12 

35.14 





1.77 

61.43 

63.22 

43.58 





1.77 

43.58 


l___ 



Diff. 

59.66 

19.64 



Latitude left 51° 25' N. 

Difference of latitude 59.66 miles = 1° 00' S. 


In latitude 50° 25' N. 






































SEO. III'.} 


TRAVERSE SAILING. 


209 


Then, by formulas for the solution of right-angled tri 
angles, we have, 


As A 6r, diff. lat. ar. c. 8.224317 
: departure 19.64 1.293141 
: : radius, 10.000000 


As sin course ar. c. 
: radius 

: : departure 19.64 


.504995 

10.000000 

1.293141 


tang course 18° 13' 9.517458 


: distance 


62.83 1.798186 


Therefore the direct course is S. 18° 13' E., and the 
distance 62.83 miles. 


OF PLOTTING. 

16. There is yet another method of finding the direct 
course and distance, much practiced by seamen, although 
it does not afford a high degree of accuracy. It is a 
method by plotting, which requires the use of a mariner’s 
scale and a pair of dividers. 

One of the scales marked on the mariner’s scale, is a 
scale of chords, commonly called a scale of rhumbs, being 
divided to every quarter point of the compass; and there 
is also a second scale of chords divided to degrees. Both 
of these scales are constructed in reference to the same 
common radius, so that the chords on the scale of rhumbs 
correspond to those on the scale of marked chords. The 
manner of using the scales will appear in plotting the last 
example. 

To construct this traverse, describe a circle with a radius 
equal to the chord of 60° and draw the meridian NS. 
Then take from the line of rhumbs the chord of the first 
course 2J points, and apply it from S to 1, to the right of 
NS ) since the course is southeasterly, and draw Al ; take, 
in like manner, the chord of the second course, 6 points, 
from A to 2, and lay it off also to the right of the meri¬ 
dian line. Apply the chord of the third course, 5| points, 
from S to 3, to the left of the meridian ; the fourth course, 
7J- points from N to 4, to the left of NS, this course be¬ 
ing northwesterly; and, lastly, apply the chord of the fifth 
course, 5-J points, from S to 5, to the right of N ( \ and 
join all the lines as in the figure. 

14 







210 ELEMENTS OF SURVEYING. [BOOK V. 

In the direction Al, lay off tlie distance ATI= 16 miles 
from a scale of equal parts, and through the extremity H, 
draw IiO parallel to A 2, and lay off IiC = 23 miles. Draw 
CD parallel to AS, and lay off CD — 36 miles ; then draw 
DE parallel to A4, and lay off 12 miles; and lastly, draw 
EF parallel to A5 , and lay off' 41 miles, and F will be the 
place of the ship. Hence, we conclude that AF is the dist¬ 
ance made good, and G AF is the course. 

Applying, then, the distance AF to the scale of e'qual 
parts, we find it equal to 62J miles; and applying the 
chord Sa to the scale of chords, we find the course GAF 
= 18i°. 

2. A ship sails from a place in latitude 24° 32' N., and 
runs the following courses and distances, viz., 1st, S. W. 
by W. dist. 45 miles ; 2d, E. S. E. dist. 50 miles ; 3d, S. 
W. dist. 30 miles; 4th, S. E. by E. dist. 60 miles ; 5th, S. 
W. by S. i W. dist. 63 miles : required her latitude, and 
the direct course and distance from the place left to the 
place arrived at, and the construction of the traverse. 

^ ns j Lat. 22° 3' N., course S. 

1 Dist. 149.2 miles. 

3. A ship from lat. 28° 32' N. has run the following 
courses, viz., 1st, N. W. by 1ST. 20 miles; 2d, S. W. 40 miles; 
3d, N. E. by E. 60 miles; 4th, S. E. 55 miles ; 5th, W. 
by S. 41 miles; 6th, E. N. E. 66 miles : required her lat¬ 
itude, the distance made good, and the direct course, also 
the construction of the traverse. 

Ans. Dist. 70.2 miles, course E. 

4. A ship from lat. 41° 12' 1ST. sails S. W. by W. 21 
miles; S. W. £ S. 31 miles; W. S. W. £ S. 16 miles; S. 
f E. 18 miles; S. W. £ W. 14 miles; then W. £ 1ST. 30 
miles: required the latitude, the direct course, and the 
distance. 

| Eat. 40° 05', course S. 52° 49' W. 

1 Dist. 111.7 miles. 

5. A ship runs the following courses, viz.: 

1st, S. E. 40 miles; 2d, K E. 28 miles; 3d, S W. by 
W. 52 miles; 4th, N W. by W 30 miles; 5th, S. S. E 


SEC. IV.] 


PARALLEL SAILING. 


211 


36 miles; 6th, S. E. by E. 58 miles: required the direct 
course, and distance made good. 

Ans j Direct course S. 25° 59' E., or S. S. E. £ E., nearly. 

(Distance 95.87 miles. 

6. A ship sails, 1st, N. W. by W. i W. 40 miles; 2d 
N. W. by l N., 41 miles ; 3d, 1ST. by E. 16.1 miles ; and 
4th, N. E. J E. 32.5 miles : required the distance made, 
and the direct course. 

Ans. Course, 21° 54' West of North. Dist. 94.6 miles. 

These examples will, perhaps, suffice to illustrate the 
principles of plane sailing. 

The longitude, made on any course, cannot be deter¬ 
mined by these methods, for this being the arc of the 
equator intercepted between two meridians, cannot be found 
under the supposition that the meridians are parallel. 

The most simple case of finding the difference of lon¬ 
gitude is when the ship sails due east or due west: this is 
called Parallel Sailing . 


SECTION IV. 


PARALLEL SAILING. 


17. The entire theory of parallel sailing is comprehend¬ 
ed in the following proposition, viz.: 

The cosine of the latitude of the parallel , is to radius , as 
the distance run to the difference of longitude. 

Let IQH represent the equa- 
tor, and FDN any parallel of 


lance sailed, then the differ¬ 
ence of longitude will be meas¬ 
ured by IQ , the arc intercept¬ 
ed on the equator. Then, 


latitude: then, Cl will be the 
radius of the equator, and EF 
the radius of the parallel. 


Suppose FD to be the dis- # 








212 


ELEMENTS OF SURVEYING. [BOOK V 


« 


since similar arcs are to each 
other as their radii (Geom., 
Bk. V., Prop 14), we have, 
EF : Cl : : dist. FD : 
diff. long. IQ. 

But EF is the sine of PF\ 
or cosine of FI] the latitude: 
and Cl is the radius of the 
sphere: hence, 

cos lat. : R : : distance : 
diff. longitude. 


P 



18. If we denote by D the distance between any two 
meridians, measured on the parallel whose latitude is L ; 
and bv D' the distance between the same meridians meas- 
urcd on the parallel whose latitude is L\ the arcs are 
similar, and we shall have (Geom., Bk. V., Prop. 14), 

cos L : D :: cos L' : D\ 
that is, cos L : cos U : : D : D'. 

Hence, when the longitude made on different parallels is the 
same , the distances sailed are proportional to the cosines of the 
parallels of latitude. 


19. By referring to Th. Y., Bk. L, we see that in any 
right-angled triangle 


R : cos angle at base : : hyp. : base, 
or cos E : R : : EC : EG; 
and by comparing this with the propor¬ 
tion, 

cos lat. : R : : dist. : diff. long; 
we see, that if in a right-angled triangle 
the angle at the base be made equal to 
the latitude of the parallel, and the base 
to the distance run ; then, the hypothenuse will represent 
the difference of longitude. 



It follows therefore, that any problem in parallel sail 
ing, may be solved as a simple case of plane sailing. For, 
if we regard the latitude as the course, the distance run 
as the base, the difference of longitude will be the hypo¬ 
thenuse of the corresponds-g right-angled triangle. 










SEC. IV.] 


PARALLEL SAILING. 


213 


EXAMPLES. 


1. A ship from latitude 53° 56 1ST., longitude 10° 18' 
E., has sailed due west, 236 miles : required her present 
longitude. 


By the rule 
As cos lat. 58° 56' 
: radius 

: : distance 236 . 

: diff long. 400.8 
Long, left 


ar. c. . .230087 

. 10.000000 

. 2.372912 


2.602999 


10° 18' E. 


400 

Biff. long. = -gjj-' degrees = 6° 40' W. 


Long. . . 3° 38' E. 


2. If a ship sails E. 126 miles from the North Cape 
in lat. 71° 10' 1ST., and then due N., till she reaches lat. 
73° 26' N.; how far must she sail W. to reach the meri¬ 
dian of the North Cape? 

Here the ship sails on two* parallels of latitude, first on 
the parallel of 71° 10', and then on the parallel of 73° 26', 
and makes the same difference of longitude on each parallel. 

Hence, by Art. 18, 

As cos lat. 71° 10' arith. comp. 0.491044 
: distance 126 . . 2.100371 

: : cos lat. 73° 26' . . 9.455044 

: distance 111.3 . . 2.046459 


3. A ship in latitude 32° N. sails due E. till her dif¬ 

ference of longitude is 384 miles: required the distance 
run. Ans. 325.6 miles. 

4. If two ships in latitude 44° 30' N., distant from 
each other 216 miles, should both sail directly S. till their 
distance is 256 miles, what latitude would they arrive at? 

Ans. 32° 17' N 


** i. 











214 


)$■ i'> 


# £ & 

NAVIGATION. 


[BOOK V 


5. Two ships in the parallel of 47° 54' N., have 9° 35' 
difference of longitude, and they both sail directly S., a 
distance of 836 miles: required their distance from each 
other at the parallel left, and at that reached. 

Arts. 385.5 miles, and 479.9 miles 




4 v 'ft t 

lJU 

t , J / y * t /» \y ✓ *- 

SECTION V. 

/ 

MIDDLE LATITUDE SAILING. 


20. Having seen how the longitude which a ship makes 
when sailing on a parallel of latitude may be determined., 
we come now to examine the more general problem, viz., 
to find the longitude which a ship makes when sailing 
upon any oblique rhumb. 

There are two methods of solving this problem, the one 
by what is called middle latitude sailing , and the other by 
Mercator’s sailing. The first of these methods is confined 
in its application, and is moreover somewhat inaccurate 
even where applicable; the second is perfectly general, and 
risrorouslv true; but still there are cases in which it is advi- 
sable to employ the method of middle latitude sailing, in 
preference to that of Mercator’s sailing. It is, therefore, 
proper that middle latitude sailing should be explained, 
especially since, by means of a correction to be hereafter 
noticed, the usual inaccuracy of this method may be 
rectified. 

Middle latitude sail¬ 
ing proceeds on the 
supposition that the de¬ 
parture or sum of all 
the meridional distan¬ 
ces, b% c'c, d'd, &c., 
from 0 to T, is equal 
to the distance M'M 
between the meridians 
passing through 0 and r i\ measured on the parallel of lati¬ 
tude equally distant from 0 and T. 










SEC. V.J MIDDLE LATITUDE SAILING. 


215 


The middle latitude is half the sum of the two extreme 
latitudes, if they are both of the same name, and half 
their difference, if the} 7- are of contrarj^ names. 

The supposition above becomes very inaccurate when the 
course is small, and the distance run great; for it is plain that 
the middle latitude distance will receive a much greater acces¬ 
sion than the departure, if the track OT cuts the successive 

meridians at a very small angle. 

\ 

The principal approaches nearer to accuracy as the angle 
0 of the course increases, because then as but little ad¬ 
vance is made in latitude, the several component depart¬ 
ures lie more in the immediate vicinity of the parallel M'M. 
But still, in very high latitudes, a small advance in lat¬ 
itude makes a considerable difference in meridional dist¬ 
ance ; hence, this principle is not to be used in such lat¬ 
itudes, if much accuracy is required. 

By means, however, of a small table of corrections, con 
structed by Mr. Workman , the imperfections of the middle 
latitude method may be removed, and the results of it ren¬ 
dered in all cases accurate. This table we have given at 
the end of this work. 

21. The rules for middle latitude sailing may be thus 
deduced. 

We have seen, in the first case of plane 
sailing, that if a ship sails on an oblique 
rhumb from 0 to T. that the hypothenuse 
OT will represent the distance; OT' the 
difference of latitude, and T'T, the depart¬ 
ure. Now, by the present hypothesis, 
the departure T'T is equal to the middle 
parallel of latitude between the meridians 
of the places sailed from and arrived at: 
so that the difference of longitude of these two places is the 
same as if the ship had sailed the distance T'T on the mid¬ 
dle parallel of latitude. The determination of the differ¬ 
ence of longitude is, therefore, reduced to the case of par¬ 
allel sailing: for, T'T now representing the distance on the 
parallel, if the angle T'TO' be made equal to the latitude of 


O' 



o 





216 


NAVI t> A TION. 


[BOOK V. 


that parallel, we shall have, by the last case, the difference 
of longitude represented by the hypothenuse O'T. We 
therefore have the following theorems: 

I. In the triangle O'TT ', 

cos O'TT' : TT' :: R : TO '; 

that is, 

cos mid. lat. : departure : : R : diff. longitude. 

II. In the triangle O'TO 

sin O' : OT : : sin 0 : O'T ; 
that is, since sin O' = cos O'TT' 

cos mid. lat. : distance :: sin. course : diff. longitude. 

III. In the triangle OTT', we have 

R : tangent 0 : : OT' : TT '; 

comparing this with the first proportion, and observing 
that the extremes of this are the means of that, we have 

OT' : O'T : : cos O'TT' : tang 0\ 

that is, 

diff. lat. : diff. long. : : cos mid. lat. : tang course. 

These three propositions comprise the theory of raid 
die latitude sailing; and when to the middle latitude sail 
ing, the proper correction, taken from Mr. Workman’s table, 
is applied, these theorems will be rendered accurate. 

In the table of pages 93 and 94, the middle latitude is 
to be found in the first column to the left. Then, along 
the horizontal line, and under the given difference of lat¬ 
itude, is inserted the proper correction to be added to the 
middle latitude to obtain the latitude in which the meri¬ 
dian distance is accurately equal to the departure. Thus, 
if the middle latitude be 37°, and the difference of latitude 
18°, the correction will be found on page 94, and is equal 
to 0° 40'. 


EXAMPLES. 

1. A ship, in latitude 51° 18' N., longitude 22° 6' W., 
is bound to a place in the S. E. quarter, 1024 miles dis¬ 
tant, and in lat. 37° 1ST.: what is her direct course and dis- 


SEC. V.] 


MIDDLE LATITUDE SAILING. 


217 


tance, as also tlie difference of longitude between tlie two 
places ? 

Lat. from 51° 18' N. ) . 

Sum of latitudes . . 88° 18' 


Lat. to 87° 0 K 


Mid. lat. 


. 44° 9' 


Diff. lat. 14° 18 = 858 miles. 


As distance 1024 
: radius 

: : diff. lat. 858 


6.989700 

10.000000 

2.933487 


. cos course 83° 5' 9.923187 


Cos mid lat 44° 9' ar c 0.144167 
: tang course 33° 5' 9.813899 
: : diff. lat. 858 2.933487 


: diff. long. 779 


2.891553 


In this operation the middle latitude has not been cor¬ 
rected, so that the difference of longitude here determined 
is not without error. To find the proper correction, look 
for the given middle latitude, viz., 44° 9', in the table of 
corrections, the nearest to which we find to be 45° ; against 
this and under 14° diff. of lat. we find 27'; and also, under 
15° we find 31', the difference between the two being 4'; 
hence, corresponding to 14° 18' the correction will be about 
28'. Hence, the corrected middle latitude is 44° 87' r 
therefore, 

Cos ^popected mid. lat. 44° 37' ar. comp. 0.147629 
ytiipg. course ^H A 33° 5'$. . 9.813899 •; 

:: diff lat. 858 . . . 2.988487 


t i 6' 




diff. long 


t' * 111 

4 f * SS , ) i *'**'/ ? 

, 7S68 , 

I y • fr, - 


JJ * ■ > . \ 


2.895015 




, r- 


3S, 


therefore, the error in the former result is about 6^- miles 

2. A ship sails in the 1ST. W. quarter, 248 miles, till her 

departure is 185 miles, and her difference of longitude 310 

miles: required her course, the latitude left, and the lat- 

^ ’ / T*/ 

ltude come to. >; ' ^ / 


/m 


a„A 0##QJ/*2 o 59 W.j • 

■) Lk 27' N.; lat. in 65° 55' N. 

S’. 'A ship, from 'latitude 37° 1ST., longitude 9° 2' W., 
aaviiig sailed between the M. and W., 1027 miles, reckons 




that she has made 564 miles of departure : what was her 
direct course, and the latitude and longitude reached? 

, j Course N. 33° 19' W., or N. W. nearly; 

**’ * Lat. 51° I S K; long. 22° 8' W. 











218 


If A VIG AT ION 


[BOOK V 


4. Required the course and distance from the east point 
of St. Michael’s, lat. 87° 48' N., long. 25° 18' W., to the 
Start Point, lat. 50° 18' hi., long. 3° 38' W. ; the middle 
latitude being corrected by Workman’s table. 
i/t - - • / Ans. Course 1ST. 51° 11' E.; dist. 1189 miles. 

tz/XC ■ / (/ / / . , 

mercator’s sailing. 

i , 22. It . litis already been observed, that when a _ship 
3ails on an oblique rhumb, the departure, the difference of 
latitude, and the distance run, are truly represented by 
the sides of a right-angled triangle. 

Thus, if a ship sails from A to B, the 
departure B'B will represent the sum of 
all the very small meridian distances, 
or elementary departures, b'b , p"p, &c.; 
the difference of latitude AB' will re¬ 
present, in like manner, the small dif¬ 
ferences of latitude Ab ', b'p\ &e.; and 
the hypothenuse vl.Z>, will express the 
sum of the distances corresponding to 
these several differences of latitude 
and departure. Each of these elements is supposed to be 
taken so small, as to form on the surface of the sphere a 
series of triangles, differing insensibly from plane triangles. 

Let ABB' be a triangle, in which the angle A repre¬ 
sents the course, AB the difference of latitude, B'B the 
departure, and AB the distance run. Produce the side 
AB' to C , until CC' shall be equal to the difference of 
longitude of the two extremities of the course : then, for 
the sake of distinction, we call 

AB' — the proper difference of latitude, 

A O' = the meridional difference of latitude, 
and we are now to explain the manner of constructing a 
table, called a table of meridional parts, which will furnish 
the meridional differences of latitude when the proper differ¬ 
ences are known. 

Let Ab'b represent one of the elementary triangles; b'b 
will then be one of the elements of departure; and Ab’ 
the corresponding difference of latitude. Now, as b'b is a 
small arc of a parallel of latitude, it is to a portion of the 









SEO. Vt] 


MERCATOR’S SAILING 


219 


equator containing an equal number of degrees, as the co-’ 
sine of its latitude is to radius (Art. 17). This similar 
portion of the equator, is the difference of longitude be¬ 
tween b' and b. 

Suppose, now, that Ab' is prolonged to p\ making p’p 
equal to the difference of longitude between b and b' : then 

bb' : pp' : : cos lat. b'b : R (Art. 17.) 

But, by similar triangles, we have 

bb' : pp' : : Ab' : Ap\ 
and consequently, 

proper lat. Ab' : mer. diff. of lat. Ap' : : cos lat. bb' : 1. 

Denoting the proper difference of latitude by d , the 
meridional difference of latitude by D, the latitude of b'b 
by l, and the radius by 1, which is, indeed, the radius of 
the table of natural sines, we shall have 

d : B : : cos l : 1, 

which gives 

I) — d secant L since —= ge c ( I . 

cos l 

If then, we know the latitude l of the beginning of a 
course, and the proper difference of latitude d of the ex¬ 
tremity of the course, we can easily find the meridional 
latitude D corresponding to that course. 

The determination of AC which represents the meri¬ 
dional difference of latitude, involves the determination of 
all the elementary parts, on which it depends. If d be 
taken equal to 1', we shall have from the equation above 
D = V sec. Z, or D = sec. 1, 

it being understood that l expresses minutes or geographi¬ 
cal miles. 

From this equation, the value of D, corresponding to 
every minute of l, from the equator to the pole, may be 
calculated ; and from the continued addition of these, there 
may be obtained, in succession, the meridional parts cor¬ 
responding to 1', 2', S', 4', &c., of proper latitude, and when 
registered in a table, they form a table of meridional parts, 
given in all books on Navigation. 

The following may serve as a specimen of the manner 
m which such a table may be constructed, and, indeed, of 
the manner in which the first table of meridional parts was 



NAVIGATION. 


0 

220 


[BOOK V 


actually formed by Mr. Wright, the proposer of this valu 
able method. 

Mer. pts. of l 7 — nat. sec. 1'. 

Mer. pts. of 2 7 = nat. sec. 1' 4- nat. sec. 2 7 . 

Mer. pts. of 3' = nat. sec. 1 + nat. sec. 2 4- nat. sec. 3'. 

. Mer. pts. of 4' = nat. sec. 1' + nat. sec. 2' 4- nat. sec. 3' + &c. 

Hence, by means of a table of natural secants we hare 

Nat. Secs. Mer. Pts. 

Mer. pts. of V = \ 1.000000 = 1.0000000 

Mer. pts. of 2 7 = 1.0000000 + 1.0000000 = 2.0000002 

Mer. pts. of 3' = 2.0000002 + 1.0000004 = 3.0000006 

Mer. pts. of 4' = 3.0000006 + 1.0000007 = 4.0000013, &c. 

There are other methods of construction, but this is the 

* ' 

most simple and obvious. The meridional parts thus de¬ 
termined, are all expressed in geographical miles, because 
in the general expression 

B — V sec. 1, 

V is a geographical mile. 

23. Having thus formed the table of meridional parts, 
if we find from it, the meridional parts corresponding to 
the latitudes of the place left and the place arrived at, 
their difference will be the meridional difference of lat¬ 
itude, or the line AC in the diagram. The difference of 
longitude denoted by C'C may then be found by the fol¬ 
lowing proportion. 

I. As radius is to the tangent of the course , so is the meri - 
dional difference of latitude to the difference of longitude. 

But if the departure be given instead of the course, then, 

II. Ms the proper difference of latitude is to the departure , 
so is the meridional difference of latitude to the longitude. 

Other proportions may also be deduced from the diagram. 

EXAMPLES. 

As an example of Mercator’s or rather Wright’s, sailing, 
let us take the following: 

1. Required the course and distance from the east point 
of St. Michael’s to the Start point: the latitudes being 37° 
48 N., and 50° 13' N., and the longitudes 25° 13' W, and 
3° 38' W. 


SEC. V.] 


MERCATOR’S CHART. 


221 


Start Point, lat. 50° 13' N. Mer. pts. 3495 

St. Michael’s, lat. 37° 48' N. Mer. pts. 2453 

Proper difference of lat. 12° 25' Mer. diff. 1042 

12 Diff. of long^T- 35' 

vDiff. in miles 745 60 

Diff. in miles 1295 


C'_ _ c 

Now, let ns suppose that we have 
sailed from A to B: we shall then 
know AB' equal proper diff. lat. = 745 
miles; A O' — meridional diff. of lat. = 

1042 ; and G'G = the difference of lon¬ 
gitude equal to 1295 miles. It is re¬ 
quired to find the course B'AB, and the 
distance AB. 

A 


For the Course. For the Distance. 


As AG' 

1042 6.982132 

1 As cos A 

51° 11' 

0.202850 

: radius 

10.000000 

: AB' 

745 

2.872156 

:: G'G 

1295 3.112270 

: : radius 


10.000000 

: tang. A 51° 11' E. 10.094402 

: AB 

1189 

3.075006 


2. A ship sails from latitude 37° N. longitude 22° 56' 
W., on the course N. 33° 19' E.: till she arrives at 51° 
18' N.: required the distance sailed, and the longitude ar¬ 
rived at. Ans. Dis. 1027 miles; long. 9° 45' W 

Mercator’s chart. 

24. Mercator’s Chart is a Map constructed for the use 
of Navigators. In this chart all the meridians are repre¬ 
sented by straight lines drawn parallel to each other, and 
the parallels of latitude are also represented by parallel 
straight lines drawn at right-angles to the meridians. 

The chart may be thus constructed. Draw on the lower 
part of the paper a horizontal line to represent the parallel 
of latitude which is to bound the southern portion of the 
chart. From a scale of equal parts, corresponding in size 



















222 


NAVIGATION. 


[BOOK V 


to the extent of the map to be made, lay off, on this line, 
any number of equal distances, and through the point? 
draw a series of parallels to represent the meridians. 

Then draw a line on the side of the map, and for the 
second parallel of latitude, find from the table of rneri 
dional parts the meridional difference of latitude corres 
ponding to the degrees between the first and second par¬ 
allel, and lay off this distance for the interval between* the 
two parallels. Then find the meridional difference between 
the second and third, and lay it off in the same way for 
the third parallel, and so on, for the fourth, fifth, &c. 

A place whose latitude and longitude are known, may 
be laid down in the same manner; for it will always be 
determined by the intersection of the meridian and parallel 
of latitude. 

If the chart is constructed on a small scale, the divisions 
on the graduated lines, may be degrees instead of minutes; 
and the meridians and parallels may be drawn only for 
every fifth or tenth degree. 

We have already seen (Art. 23), that the meridional 
difference of latitude bears a constant ratio to the difference 
of longitude, so long as the course remains unchanged: 
and hence we see that on Mercator’s chart, every rhumb 
will be represented by a straight line. 

LINE OF MERIDIONAL PARTS ON GUNTER’S SCALE. 

25. This scale corresponds exactly with the table of me¬ 
ridional parts, excepting, that in the table, the circle is divid 
ed to minutes, while the scale is divided only to degrees, 
A scale of equal parts is placed directly beneath the scale 
of meridional parts; if the former corresponds to divisions 
of longitude, the latter will represent those of latitude. 
Hence, a chart may be constructed from those scales, by 
using the scale of equal parts for the lines of longitude, 
nd the scale of meridional parts for those of latitude. 


A TABLE 



OF 


LOGARITHMS OF NUMBERS 

FROM 1 TO 10,000. 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

£ 

0-000000 

26 

i- 4 i 4973 

5 i 

1-707670 

76 

1-880814 

2 

o- 3 oio 3 o 

27 

i • 4-3 1 364 - 

52 

1-716003 

77 

1-886401 

3 

0-477121 

28 

1-447108 

53 

1-724276 

7 « 

1-892095 

4 

0-602060 

29 

1-462398 

54 

1-732394 

79 

1-897627 

5 

0-698970 

3 o 

1-477121 

55 

1 -74o363 

80 

1-903090 

6 

0-778151 

3 i 

1-491362 

56 

1-748188 

81 

1-908480 

7 

0-845098 

32 

1- 5 o 5 i 5 o 

5 i 

1-755875 

82 

1•913814 

8 

0-908090 

33 

1• 5 1 85 14 

08 

1-763428 

83 

1-919078 

9 

0-95424.3 

34 

1- 53 i 479 

5 9 

1-770852 

84 

1-924279 

IO 

1•000000 

35 

1*544068 

60 

1-778151 

85 

1-929419 

11 

1-041393 

36 

1- 5563 o 3 

6l 

i-78533o 

86 

1-934498 

12 

1-079181 

37 

1 -568202 

62 

1-792392 

87 

1-939519 

i 3 

1•11 3943 

38 

1-579784 

63 

1-799841 

88 

1 • 9444-33 

£4 

1-146128 

3 9 

1-591065 

64 

1-806181 

89 

1•949390 

i 5 

1•176091 

40 

1-602060 

65 

1-812913 

90 

1-954243 

16 

I-204>20 

41 

1-612784 

66 

1-819544 

91 

1-959041 

17 

1-230449 

42 

1 -6232.49 

67 

1-826075 

92 

1-968788 

18 

1 -255273 

43 

1-633468 

68 

1-832509 

9 3 

1•968483 

*9 

20 

1-278754 

1- 3 oio 3 o 

44 

45 

1 -643453 

1 - 653 21 3 

69 

70 

1-838849 

1-845098 

9 5 

1-973128 
1-977724 

21 

1-322219 

46 

1-662758 

7 i 

1- 85 i 258 

96 

i-982271 

22 

1 -342423 

47 

1-672098 

72 

1-857333 

97 

1-986772 

23 

i -361728 

48 

1-681241 

73 

1 -863323 

98 

1-991226 

24 

i-380211 j 

49 

1-690196 

74 

1-869232 

99 

1-990680 

25 

1-397940 | 

5 o 

1-698970 

7 ^ 

1-870061 

100 

2•000000 


Remark. In the following table, in the nine right hand 
columns of each page, where the first or leading figures 
change from 9’s to 0’s, points or dots are introduced in 
stead of the 0’s, to catch the eye, and to indicate that from 
thence the two figures of the Logarithm to be taken from 
the second column, stand in the next line below 







































2 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. I 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D.l 

i 

IOO 

000000 

04.34 

0868 

i3oi 

1734 

2166 

25 9 8 

3029 

3461 

3891 

432 j 

IOI 

4321 

4751 

5181 

5609 

6o38 

6466 

6894 

7321 

7748 

8174 

428 

102 

8600 

9026 

945i 

9876 

°3oo 

0724 

1147 

1670 

i 99 3 

2410 

424 ! 

i io3 

oi2~837 

3259 

368o 

4100 

4521 

4940 

536o 

5 779 

6197 

6616 

419 

104 

7o33 

7451 

7868 

8284 

8700 

9116 

o53 3 

9947 

°36i 

® 77 5 

4161 

; ioo 

021189 

i6o3 

2016 

2428 

2841 

3252 

3664 

4075 

4486 

4896 

412 

106 

53 06 

5715 

6i25 

6533 

6942 

735o 

7757 

8164 

8571 

8978 

408 

107 

9 384 

9789 

*195 

•600 

1004 

1408 

1812 

2216 

2619 

3021 

404 

108 

o33j24 

3826 

4227 

4628 

5029 

543o 

583o 

623o 

6629 

7028 

400 

109 

7426 

7825 

8223 

8620 

9017 

9414 

9811 

®207 

®6o2 

•998 

3 9 6 

110 

041393 

1787 

2182 

2076 

2969 

3362 

3755 

4U8 

4540 

4932 

*3 9 3 

111 

5323 

5 7 i4 

6io5 

6495 

6885 

7270 

7664 

80 5 3 

8442 

883o 

389 

112 

113 

9218; 9606 
003078 3463 

9093 

3846 

°38o 

423o 

®766 

46i3 

1153 
4996 

1538 
5378 

1924 

5760 

23o 9 

6142 

2694 

6524 

386 

382 

114 

6905 

7286 

7666 

8046 

8426 

88o5 

9185 

g 563 

9942 

®32o 

379 

1 1 5 

060698 

1075 

1452 

1829 

2206 

2582 

2 9 58 

3333 

3709 

4083 

376 

116 

4458 

4832 

5206 

558o 

5g53 

6326 

6699 

7071 

7443 

7815 

3 7 2 

117 

8186 

8557 

8928 

9298 

9668 

°®38 

•407 

*776 

1145 

1014 

369 

118 

071882 

2250 

2617 

2980 

3352 

3718 

4o85 

4451 

4816 

0182 

36o 

119 

5547 

6912 

6276 

6640 

7°°4 

7368 

7731 

8094 

8457 

8819 

363 

I 20 

079181 

9543 

9904 

*266 

*626 

*987 

i347 

1707 

2067 

2426 

36o 

121 

082785 

3144 

35o3 

386i 

4219 

4576 

4 9 34 

0291 

5647 

6004 

3o 7 

122 

636o 

6716 

7071 

7426 

7781 

8136 

8490 

8845 

9198 

96^2 

355 

123 

9905 

®258 

®6i 1 

°963 

1315 

1667 

2018 

2870 

2721 

3071 

35i 

124 

093422 

3772 

4122 

4471 

4820 

5169 

55 i 8 

5866 

6215 

656? 

349 

125 

6910 

7207 

7604 

79 5i 

8298 

8644 

8990 

9335 

9681 

®»26 

346 

126 

100871 

0715 

1059 

i4o3 

1747 

2091 

2434 

2777 

3119 

3462 

343 

127 

3 804 

4146 

4487 

4828 

5i6 9 

55io 

5851 

6191 

6531 

6871 

34o 

128 

7210 

7549 

7888 

8227 

8565 

8 9 o3 

9241 

9079 

9916 

°253 

338 

129 

110690 

0926 

1263 

1599 

1934 

2270 

26o5 

2940 

3275 

36o 9 

335 

i3o 

1i3g43 

4277 

4611 

4944 

6278 

56 11 

5 9 43 

6276 

6608 

6940 

333 

131 

V-V 

7603 

7934 

8265 

85 9 5 

8926 

9266 

9086 

99 1 5 

°245 

33o 

132 

i2o5->4 

0903 

I 23 I 

156o 

1888 

2216 

2544 

2S71 

3198 

3525 

328 

1 33 

3802 

4178 

4004 

483o 

5156 

5481 

53o6 

6131 

6406 

6781 

325 

134 

7100 

7429 

7753 

8076 

83 99 

8722 

9045 

93M 

9690 

©0,2 

323 

135 

i3o334 

o65o 

°977 

1298 

1619 

i 9 3o 

2260 

258o 

2900 

3219 

321 

136 

3539 

3858 

4177 

4496 

4814 

5133 

545i 

5769 

6086 

6403 

318 

137 

6721 

7o3 7 

7354 

7671 

79 8 7 

83 o3 

8618 

8984 

9249 

9564 

315 

138 

9870 

® 194 

•5o8 

•822 

1136 

i45o 

1768 

2076 

238 9 

2702 

314 

139 

t 43o15 

3327 

363 9 

3 9 5i 

4263 

4574 

4885 

5196 

55o7 

5818 

311 

140 

146128 

6438 

6048 

7o58 

7367 

7676 

7980 

8294 

S6o3 

8911 

309 

141 

92 1 9 

9627 

9835 

®I42 

•449 

•i56 

io63 

1370 

1676 

1982 

307 

142 

162288 

2094 

2900 

32o5 

35io 

3S15 

4120 

4424 

4728 

5o32 

3o5 

143 

5336 

5640 

5g43 

6246 

6049 

6852 

7154 

7457 

77^9 

8061 

3o3 

144 

8362 

8664 

8965 

9266 

9067 

9868 

«“i68 

•469 

*769 

1068 

3oi 

145 

161368 

1667 

1967 

2266 

2564 

2863 

3161 

3460 

3 7 58 

4o55 

299 

146 

4353 

465o 

4947 

5244 

5541 

5838 

61 34 

643o 

6726 

7022 

297 

U 7 

7317 

76i3 

7908 

82o3 

8497 

8792 

9086 

938o 

9674 

9968 

295 

148 

170262 

o555 

0848 

1141 

1434 

1726 

2019 

2311 

26o3 

2895 

293 

149 

3186 

3478 

3769 

4060 

43 51 

4641 

4 9 32 

5222 

5512 

58o2 

291 

i5o 

176091 

638i 

6670 

6959 

7248 

7536 

7820 

8113 

8401 

8689 

289 

1 5 1 

8977 

9264 

9552 

9839 

*126 

• 4 1 3 

•699 

•985 

1272 

1 55 a 

287 

15a 

181844 

2129 

2415 

2700 

2q85 

3270 

3555 

3 83 9 

4 i 23 

4407 

280 

153 

4691 

4970 

5259 

5542 

5820 

6108 

63 9 i 

6674 

6906 

7239 

283 

1 54 

7021 

7803 

8084 

8366 

8647 

8928 

9209 

9 4qo 

9771 

®*5i 

281 

1 55 

,190332 

0612 

0892 

1171 

1401 

u3o 

2010 

2289 

2067 

2S46 

279 

r56 

3125 

34o3 

368 1 

3959 

j 4237 

45 1 4 

479' 2 

5o6 9 

5346 

5623 

278 

167 

J 58o<; 

6176 

6453 

6729 

; 7000 

7281 

7 556 

7832 

8107 

8382 

276 

j 158 

1 8607 

8932 

j 9206 

q4<8 i 

9755 

®®2 9 

°3o3 

®5 77 

®85o 

1124 

274 

: 59 

j 201397 

1670 

! 1943 

; 2216 

2488 

j 2761 

3o33 

33o5 

3577 

3848 

272 

N. 

| 

i i ) 

{ 

! 1 

i 

* 2 

1 

3 

I 4 

3 

! 6 

7 

8 

9 

D . 
















































































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


8 


N. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

160 

204120 

4391 

4663 

4934 

5204 

5475 

5746 

6016 

6286 

65*56 

271 

j6i 

6826 

7096 

7365 

7634 

79°4 

8173 

8441 

8710 

8979 

9247 

269 ! 

162 

9015 

9733 

*®5i 

®3ig 

®5S6 

®853 

1121 

1338 

1604 

1921 

2.67, 

163 

212188 

2454 

2720 

2986 

3252 

35i8 

3783 

4049 

4314 

4379 

266 

164 

4844 

5109 

53 7 3 

5638 

0902 

6166 

643o 

6694 

6907 

7 22X 

264 

i65 

7484 

7747 

8010 

8273 

8536 

8798 

9060 

9828 

9580 

9346 

262 

166 

220108 

0370 

o631 

0892 

1153 

1414 

1675 

1986 

2196 

2406 

261 

167 

2716 

2976 

3236 

3496 

3705 

4oi5 

4274 

4033 

4792 

3031 

2 oc, 

168 

5309 

5563 

5826 

6084 

6342 

6600 

6858 

7110 

7372 

7 63o 

208 

169 

7887 

8144 

8400 

8607 

8 qi 3 

9170 

9426 

9682 

9938 

*193 

2.36 

170 

230449 

0704 

0960 

1215 

1470 

1724 

i?79 

2234 

2488 

2742 

204 

Hi 

2996 

3200 

3 oo 4 

37 r G 

1 4011 

4264 

4017 

4770 

5o23 

5276 

2 53 

172 

5528 

5781 

6o33 

6285 

6537 

6789 

7041 

7292 

7044 

779 8 

202 

. *73 

8046 

8297 

8048 

8799 

9049 

9299 

g55o 

9800 

e©5o 

®3oo 

200 

1 H4 

240049 

0799 

1048 

1297 

i 546 

1790 

2044 

2293 

254x 

2790 

249 

i 7 5 

3o38 

3286 

3534 

8782 

4o3o 

4277 

4025 

4772 

Soig 

0266 

248 

176 

5313 

5709 

6006 

6202 

6499 

6745 

6991 

7237 

7482 

7728 

246 

177 

7973 

8219 

8464 

8709 

8904 

9198 

9443 

9687 

9932 

e x 7 6 

240 

178 

200420 

0664 

0908 

1151 

i3g5 

1638 

1881 

2125 

2368 

261c 

243 

*79 

*853 

3096 

3338 

358o 

3822 

4064 

43 06 

4548 

479° 

5o3i 

242 

180 

255273 

5514 

5755 

5 99 6 

6237 

6477 

6718 

6o58 

7198 

7439 

241 

181 

7679 

7918 

8158 

8398 

8637 

8877 

9116 

9305 

9394 

9830 

23 9 

182 

260071 

oiio 

0048 

0787 

1025 

1263 

15o 1 

1739 

1976 

22)4 

238 

183 

2451 

2688 

2920 

3162 

3399 

3636 

38 7 3 

4109 

4346 

4582 

s3 7 

184 

4818 

5 o 54 

6290 

5525 

5761 

5996 

6232 

6467 

6702 

6937 

235 

234 

' 185 

7172 

7406 

7641 

7870 

8110 

8344 

85 7 8 

8812 

9046 

9279 

186 

9013 

9746 

9980 

®2 i 3 

*446 

*679 

®9I2 

1144 

i3 77 

1609 

233 

1S7 

271842 

2074 

23oo 

2538 

2770 

3ooi 

3233 

3464 

3696 

3927 

232 

188 

4i 58 

4389 

4620 

485 o 

5o8i 

5311 

5542 

5772 

6002 

6232 

23 o 

189 

6462 

6692 

6921 

7151 

733o 

7609 

7 833 

8067 

8296 

8320 

229! 

190 

278754 

8982 

9211 

9439 

9667 

9890 

®123 

*35i 

®5 7 8 

®8o6 

228 

191 

28io33 

1261 

1488 

1715 

1942 

2169 

2396 

2622 

2849 

3o 7 3 

2271 

192 

3Joi 

3027 

8703 

8979 

42o5 

4431 

4606 

4882 

5107 

5332 

226 j 

193 

5557 

0782 

6007 

6232 

6406 

6681 

6905 

7180 

7354 

7 5 7 8 

22 !>j 

194 

7S02 

8026 

8249 

8473 

8696 

8920 

9143 

g3 66 

9- a 9 

9312 

223 ! 

195 

290030 

0207 

0480 

0702 

0925, 

1147 

1369 

1591 

18 x 3 

2o34 

222 

196 

• 2256 

247*8 

2699 

2920 

3i4i 

3363 

3584 

38o4' 

4020 

4246 

221 

197 

4466 

4687 

4907 • 

0127 

5347 

5567 

5787 

6007 

6226 


220 1 

198 

6665 

6834 

7104 

7323 

7042 

7761 

7979 

8 ‘ 9 o 

8416 

8630 

®8i3 

2I9| 

l 99 

8853 

9071 

9289 

9007 

9725 

9943 

°i6i 

®3 7 S 

®5q5 

j 

2i8; 

200 

3oio3o 

1247 

1464 

1681 

1898 

2114 

2331 

2547 

2764 

2980 

2I 7 

201 

31.96 

3412 

3628 

3844 

4009 

4275 

4491 

4706 

4921 

5136 

216! 

202 

5351 

5566 

5 7 8 i 

5996 

6211 

6426 

663 9 

6854 

7068 

7282 

2 (5 ! 

2 o 3 

7496: 

7110 

7924 

813 7 

83 51 

8564 

8778 

8991 

9204 

9417 

2 1 3 

204 

9630! 

9843 

©«56 

®263 

®48 i 

a 6 9 3 

®go6 

1118 

i33o 

1042 

2 X 2 

| 200 

3i17041 

1966 

2177 

2389 

2600 

2812 

3o23 

3234 

8440 

3656 

211 

206 

3867* 

4078 

4289 

4499 

4710 

4920 

5i3o 

534o 

5551 

5 7 6o 

2io 

207 

6970; 

6180 

6890 

6099 

6809 

7018 

7227 

7 436 

7646 

7804 

2,-9 

208 ! 

8o63 

8272 

8481 

8689 

8898 

9106 

9314 

9622 

9780 | 998^ 

20 O 

209 : 

320146' 

o354 

0062 

0769 

0977 

1184 

1391 

15g8 

1003 

201 2 

207 . 

210 ' 

322219' 

2426 

2633 

283 9 

3046 

3252 

3458 

3665 

38 7 I 

4077 

206 

211 1 

4282 

4483 

4694 

4899 

5io5 

53xo 

55x6 

0721 

3926 

6131 

200 | 

212 j 

6336! 

6641 1 

6745 ! 

6900 

7155 

7 35 9 

7563 

7767 

7972 

8176 

204 1 

2 1 3 

838c 

8583 

8787 j 

8991 

9194 

9 3 9 8 

9601 ! 

9800 ! 

«c?sg 

•21 x 

2o3 : 

214 ' 

33 04 

0617 

0819 1 

1022 

1220 

1427 

i63o 

1832 

2044 

2 236 

2 02 

2 I 5 | 

24381 

2640 

2842 ! 

3 044 

3246 

34^7 

3649 

3 oOO ; 

4001 

4203 

202 

216 1 

4454 

4655 

4856 ! 

6007 

5207 

5458 

5658 

5859 1 

6059 

6200 

201 

217 ; 

6460! 

6660 

6860 

7060 

7260 

7409 

7609 

7858 : 

8038 | 

820- 

200 

218 1 

8456, 

8656 ‘ 

8855 ; 

9004 

9253 

9401 | 

9600 

9849 

®°4 7 

©2/6 

I99 1 

219 

; 

340444: 

0642 

0041 I 

io3g 

i23 7 

1435 

1682 

i83o 

2028 ; 

2225 

*9® j 

—-- 

N. 1 

° i 

1 

2 

3 

4 

5 j 

6 

7 

8 1 

9 

IL 1 




15 







































































4 A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. | 

0 ! 

1 

0 

3 ! 

4 ! 

5 

6 

7 

8 

9 

D. 

220 

342423 

2620 

2817 

3oi4 I 

3212 i 

3409 

36o6 

38o2 

3999 

4196 

197 

221 

4392 

4589 

4785 

4981 I 

5178 1 

5374 

5570 

6766 

5962 

6107 

196 

222 

6353 

6549 1 

6744 

6939 1 

7 1 3^ 

733o 

7625 

7720 

79 l5 

8110 

195 

223 

83o5 

85oo 

8694 

8889 

9083 

9278 

9472 

9666 

9860 

©®54 

194 

224 

350248 

0442 

o636 

0829 ] 

1023 I 

1216 

1410 

i6o3 

1796 

i9 8 9 

198 

223 

2183 

2876 

2568 

2761 | 

2934 ! 

3147 

3339 

3532 

3724 

3 9* 6 

193 

j 2 2fc 

4108 

43 oj I 

4493 

4685 | 

4876 i 

5o68 

526o 

5462 

5643 

5834 

192 

227 

6026 

6217 

6408 

6599 

6790 i 

6981 

7172 

7363 

7554 

7744 

191 

228 

7935 

8i25 

8316 

85o6 

8696 j 

8886 

9076 

9266 

9456 

9646 

190 

229 

9 835 

*®25 

©215 

*404 1 

©593 j 

*783 

©972 

1161 

i35o 

i 539 

189 

23 o 

361728; 

1917 

2105 

2294 

2482 j 

2671 

2869 

3o48 

3236 

3424* 

188 

1 231 

36i2 

38oo 

3988 

4176 

4363 : 

435i 

4739 

4926 

5i i3 

53oi 

188 

232 

5488 

5675 | 

5862 

6049 

6236 j 

6423 

6610 

6796 j 

6 9 83 

7169 

187 

233 

7356 

7542 

7729 

7913 

8101 

8287 

8473 

8629 

8845 

9o3o 

186 

234 

9216 

9401 

9687 

9772 : 

9958 | 

©143 

©328 

- 

®5i3 

•698 

©883, 

185 

235 

371068 

1253 

1437 

l622 

1806 1 

i99i 

2170 

236 o 

2544 | 

2728 

184 

236 

2912 

3 096 1 

3280 

3464 

3647 

3831 

4010 

4198 

4382 

4565 

184 

237 

4748 

4932 1 

3115 

5298 

5481 

5664 

5846 

6029 

6212 ; 

6894 

1 S3 

238 

6577 

6759 

6942 

7124 1 

-] 3 o 6 

7488 

7670 

7862 

8o34 

8216 

182 

239 

83 9 8 

858o 

8761 

8943 

9124 

9306 

9487 

9668 

9849 

°©3o 

181 

240 

3 So 211 

0392 

0673 

0754 

0934 

1115 

1296 

U76 

1656 ] 

1837 

181 

241 

2017 

2197 

2377 

2557 

2737 

2 9 1 7 

3097 

3277 > 

3456 I 

3636 

180 

242 

38i 5 1 

3993 

4174 

4353 

4533 1 

4712 

4891 

5070 

6249 I 

5428 

179 

243 

56o6i 

5785 

5964 

6142 

6321 

6499 

6677 

6856 ! 

7034 

7212 

178 

244 

7890 

7568 

7746 

7928 

81D1 

8279 

8456 

8634 

8811 

8989 

178 

243 

9166 

9343 

9620 

9698 

9875 

©°5i 

©228 

*4 o 5 

©582 ! 

©709 

177 

246 

390935 

1112 

1288 

1464 

1641 1 

1817 

1993 

2169 

2345 | 

2521 

176 

247 

2697 

2873 

3o48 

3224 

3400 

3575 

3761 

3926 

4101 

4277 

176 

248 

4432 

4627 

4802 

4977 

5152 

5326 

55oi 

5676 

585o 

6025 

i 7 5 

249 

6199 

6374 

6548 

6722 

6896 

7071 

7245 

7419 

7692 

7766 

174 

25 o 

397940 

8114 

8287 

8461 

8634 

8808 

8981 

9164 

9328 

95oi 

i 7 3 

25 I 

9674 

9847 

c ®20 

©192 

©365 

©533 

©711 

©883 

io56 

I 228 

173 

252 

401401 

1673 

1745 

1 9 1 7 

2089 

2261 

2433 

26 o 5 

2 777 

2949 

172 

| 253 

31 2 I 

3292 

3464 

3635 

3807 

3 97 8 

4149 

4320 

4492 

4663 

171 

234 

4834 

5oo5 

5176 

5346 

55i7 

5688 

5858 

6029 

6199 

6370 

171 

I 255 

654o 

6710 

688l 

7051 

7221 

7391 

756 i 

77 3 i 

7901 

8070 

170 

256 

8240 

8410 

8379 

8749 

8918 

9087 

9207 

9426 

9090 

9764 

169 

257 

9933 

®i 02 

°27I 

©440 

•609 

*777 

•946 

1114 

1283 

I45i 

169 

[ 258 

411620 

1788 

1956 

2124 

2298 

2461 

2629 

2796 

2964 

3132 

168 

259 

33oo 

3467 

3635 

38o3 

3970 

4 i 37 

43 oo 

4472 

463g 

4806 

167 

260 

414973 

5140 

53 o 7 

5474 

564 i 

58o8 

5974 

6141 

63o8 

6474 

167 

261 

6641 

6807 

6973 

7 i3 9 

73o6 

7472 

7688 

7804 

797.° 

8135 

166 

262 

83oi 

8467 

8633 

8798 

8964 

9129 

9295 

9460 

9625 

9791 

165 

263 

9956 

®i 21 

•286 

©431 

•616 

©781 

©945 

IIIO 

1275 

1439 

165 

264 

421604 

1788 

1933 

2097 

2261 

2426 

2090 

2754 

2918 

3o82 

164 

265 

3246 

3410 

3574 

3737 

3901 

4 o 65 

4228 

4392 

4 d 55 

4718 

164 

266 

4882 

5 o 45 

5208 

5371 

5334 

5697 

586o 

6023 

6186 

6340 

i63 

267 

6511 

6674 

6836 

6999 

7161 

7324 

7486 

7648 

7811 

7973 

16: 

268 

8135 

8297 

8469 

8621 

8 t 83 

8944 

9106 

9268 

9429 

9 5 9 1 

162 

269 

9752 

9914 

*•73 

©236 

©398 

©559 

*720 

•881 

1042 

1203 

161 

270 

43I364 

1525 

1685 

1846 

2007 

2167 

2328 

2488 

2649 

2809 

161 

271 

2969 

3i3o 

3290 

345o 

36io 

8770 

3g3o 

4090 

4249 

4409 

160 

272 

4669 

4729 

4888 

5o48 

6207 

5367 

5326 

5685 

5844 

6004 

169 

273 

6i63 

6322 

6481 

6640 

6798 

6957 

7116 

7275 

7433 

7592 

109 

274 

77 5 i 

79°9 

8067 

8226 

8384 

8542 

8701 

8859 

9017 

9170 

158 

275 

9 333 

9491 

9648 

9806 

9964 

©122 

©279 

*437 

®5 9 4 

©752 

158 

276 

440909 

1066 

1224 

1381 

1538 

1695 

i852 

2009 

2166 

23»>3 

157 

*71 

2480 

2637 

2793 

2950 

3106 

3263 

3419 

3576 

3732 

388 9 

157 

278 

4o45 

4201 

4357 

1 4513 

4669 

4825 

4981 

5i 37 

5293 

5449 

i56 

279 

56o4 

5760 

6915 

1 6071 

6226 

6382 

6537 

6692 

6848 

7oo3 

155 

N. 

0 

1 

! 2 

3 

4 

5 

6 

7 

1 8 

9 

D, 

























































































A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

~!K- J 

I). 

280 

447I5? 

3 731 3 

7468 

7623 

7778 

7933 

8088 

8242 

83 9 7 

8552 

I 1 55 1 

2S1 

870^ 

> 8861 

9015 

9170 

9324 

9478 

9 633 

9787 

9941 

«® 9 5 

! 164! 

282 

45 o 24 c 

o 4 o 3 

0557 

0711 

o 865 

1018 

1172 

1 3 26 

1479 

x 633 

i 94 i 

283 

1786 

1940 

209I 

2247 

2400 

2553 

2706 

285 9 

3oi2 

i 3 1 65 

I 53 ; 

284 

33 i£ 

3471 

8624 

3777 

3 93 o 

4082 

4235 

4887 

4-640 

4692 

153 

285 

484 ^ 

4997 

5 i 5 o 

53o2 

5454 . 

56 o 6 

5 j 58 

5910 

6062 

6214 

I 52 

286 

636 t 

65 i 8 

6670 

6821 

6973 

7125 

7276 

742 fS 

7679 

7731 

I 52 1 

287 

7882 

8 o 33 

8184 

833 o 

8487 

8638 

8789 

8940 

9091 

9242 

! 5 I 

288 

9392 

9543 

9694 

9845 

9 99 5 

®i46 

°2 9 6 

°447 

® 5 9 7 

*748 

151 

289 

46089? 

1048 

1198 

1348 

U99 

1649 

1799 

1948 

2098 

2248 

i 5 o 

290 

46239? 

2548 

2697 

2847 

2997 

3 i 46 

3296 

3445 

35 9 4 

3744 

l 5 (); 

291 

3893 

4042 

IT 

434 o 

4490 

4639 

4788 

4936 

5 o 85 

5234 

149 

292 

5383 

5532 

568 o 

5829 

5 977 

6126 

6274 

6423 

65 -/I 

6719 

149 

293 

686b 

7016 

7164 

7312 

746 o 

7608 

7756 

7904 

8 o 52 

8200 

148 

294 

8347 

8496 

S64 3 

8790 

8 9 38 

go 85 

9233 

9 3 8o 

9627 

9675 

1 48 j 

295 

9822 

9969 

®i 16 

®263 

®4io 

° 55 j 

° 7°4 

® 85 i 

*998 

1 145 

147 | 

296 

471292 

1438 

1 585 

1732 

1878 

2025 

2171 

2 3 18 

2464 

2610 

146: 

297 

2706 

2903 

3 049 

3i 9 5 

334 i 

3487 

3633 

3779 

3 9 25 

4071 

1461 

298 

4216 

4362 

45 o 8 

4653 

4799 

4944 

5090 

5235 

538 1 

5526 

146 

299 

5671 

58 6 

5962 

6107 

6202 

63 9 7 

6542 

6687 

6832 

6976 

140 

3 oo 

477121 

7266 

74 ti 

7555 

7700 

7844 

7989 

81 33 

8278 

8422 

140 

- 3 oi 

8566 

8711 

I 8855 

8999 

9143 

9287 

943 1 

g 5 j 5 

9719 

9863 

144 

302 

480007 

oi 5 i 

0294 

0438 

o582 

0725 

0869 

1012 

11 56 

1299 

144 ! 

3 o 3 

1443 

1 586 

1 7 2 9 

1872 

2016 

2 l 5 9 

2302 

2445 

2588 

2 j 3 l 

143 

3 o 4 

2874 

3 oi 6 

3109 

33o2 

3445 

3587 

3730 

3872 

401 5 

4107 

U 3 j 

3 o 5 

43 oo 

4442 

4585 

4727 

4869 

5 oi r 

5 1 53 

52 9 5 

5437 

5579 

142! 

3 06 

5721 

• 5863 

6 oo 5 

6147 

6289 

6480 

6672 

6714 

6855 

6997 

142 ! 

3 o~j 

71 38 

7280 

7421 

7563 

7704 

7845 

7986 

8127 

8269 

8410 

141! 

3 o 8 

8551 

8692 

8833 

8974 

9114 

9255 

9896 

9537 

9677 

9818 

141 

309 

gg 5 B 

©®99 

®239 

® 38 o 

•520 

©661 

®8oi 

® 94 i 

1081 

1222 

140 

3 io 

491862 

i 5 o 2 

1642 

1782 

1922 

2062 

2201 

2341 

2481 

2621 

140! 

3 11 

2760 

2900 

3 o 4 o 

3179 

33 19 

3458 

3597 

3737 

3876 

4 oi 5 

i 3 9 

3 12 

41 55 

4294 

4433 

4072 

4711 

4S00 

4989 

5128 

5267 

5406 

i 3 9 

3 1 3 

5544 

5683 

5822 

5960 

6009 

6238 

6876 

65 1 5 

6653 

6791 

i 3 9 

3 14 

69 3 0 

7068 

7206 

7344 

7483 

7621 

77 5 9 

7897 

8 o 35 

8173 

i 38 

3 1 5 

83 n 

8448 

8586 

8724 

8862 

8999 

9 i3 7 

9275 

9412 

g 55 o 

1 38 

3 16 

. 9687 

9824 

9962 

®®99 

®236 

•374 

° 5 i 1 

•648 

© 7 85 

•922 

137 

317 

701009 

1196 

1 333 

1470 

1607 

1744 

1880 

2017 

21 54 

2291 

i 3 7 

3 18 

2427 

2564 

2700 

2837 

2973 

3 109 

3246 

3382 

35 18 

3655 

136 

3 ig 

3 79 i 

3927 

4 o 63 

4199 

4335 

447 1 

4607 

4743 

4878 

5 oi 4 

1 36 

320 

5 o 5 i 5 o 

5286 

5421 

5557 

5693 

5828 

6964 

6099 

6234 

6370 

1 36 

321 

65 o 5 

6640 

6776 

6911 

7046 

7181 

7816 

745 

7 586 

7721 ! 

1 35 

322 

7856 ^ 

799 1 

8126 

8260 

83 9 5 

853 o 

8664 

S799 

8984 

9068 

i 35 i 

323 

9203 

9337 

9471 

9606 

974 o 

9874 


®r 43 

«2 77 

• 4 11 

134! 

3 24 

5 1o 545 

0679 

081 3 

0947 

1081 

121 5 

1 349 

1482 

l6l6 

1760 ; 

134 , 

325 

1 883 

2017 

21 5 1 

2284 

2418 

2001 

2684 

2818 

295 l 

3 o 84 

1 33 

326 

32 i 8 

335 i 

3484 

3617 

3700 

3883 

4016 

4 M 9 

4282 

44 i 4 J 

i 33 • 

327 

4548 

4681 

481 3 

4946 

5 o 79 

5211 

5344 

5476 

56 o 9 

5741 I 

1 33 ' 

328 

58 7 4 

6006 

6139 

6271 

64 o 3 

6535 

6668 

6800 

6932 

7064 , 

1 3 

329 

7196 

7328 

7460 

7092 

7724 

7855 

79 8 7 

8119 

825 l 

8382 1 

i 3 

33 o i 

h 85 i 4 

8646 

8777 

8909 

9040 

9 1 7 1 

9 3 o 3 

9434 

9566 

9897 

1 3 1 

33 1 

9828 

99 5 9 

°®90 

®2 2I 

®353 

®484 

° 6 i 5 

®745 

©876 

1007 

i 3 i 1 

332 J 

)2i i 38 

1269 

1400 

i 53 o 

1661 

1792 

1922 

2o53 

21 83 

23 14 j 

1 3 1 j 

333 

2444 

2570 

2705 

2835 

2966 

3096 

3226 j 

3356 

3486 

36 i 6 

i 3 o 

334 

3746 

38 7 6 

4006 

41 36 

4266 

4396 

4626 ] 

4656 

4785 

49 i 5 

i 3 o 

335 

5 o 45 

5 i 74 

53 o 4 

5434 

5563 

56 9 3 

5822 

5 9 5 i 

6081 

6210 | 

129 

336 

633 9 

6469 

65 9 8 

6727 

6856 

6980 

7 ii 4 

7243 

7372 

i 5 oi 

129 

337 

763° 

77 5 9 

7888 

8016 

8 i 45 

8274 

84.02 1 

853 1 

8660 

8788 

120 

338 

8917 

9045 

9'74 

9302 

943 o 

9OO9 

9687 J 

981 5 

9943 

@<r>~ 2 

128 

339 5 

30200 

1 

o 328 

0456 j 

o 584 

0712 

0840 

0968 

1096 

1 

1223 

i 35 i 

128 

N. 

0 

1 

2 

3 

4 

5 

6 

7 i 

8 

9 1 

_L. 

D. 





















































































































8 


A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


r“-— 

N. 

0 

1 

2 

3 

4 

5 

6 

I 7 

i 8 

9 

i 

1 340 

531479 1607 

1734 

j 1862 

1990 

j 2117 

2245 

2372 

j 2500 

2627 

I 128 

34 * 

2704 28S2 

3009 

j 3 1 36 

1 3264 

I 3391 

35 i 8 

3645 

3772 

38 gg 

1 27 

842 

4026 41 53 

4280 

j 4407 

1 4534 

4661 

4787 

! 4 9 i 4 

1 6041 

5167 

1 127 

i 343 

6294 5421 

5547 

j 56 74 

58 oo 

6927 

6 o 53 

6180 

63 o 6 

6482 

J 126 

344 

6558 6685 

| 6811 

I 6 9 3 7 

I7063 

7189 

1 73 1 5 

7441 

7667 

i 7698 

1 126 

i 345 

7819 7940 

! 8071 

; 8 i97 

I 8322 

8448 

8674 

8699 

8825 

1 8 9 5 i 

126 

| 346 

9076 9202 

9327 

19452 

9078 

97°3 

9S29 

| 99 5 4 

«® 79 

«204 

125 

1 ?47 

540829 o455 

0080 

0705 

o 83 o 

0933 

1080 

1205 

i 33 o 

1454 

123 

343 

1579 1704 

! i y 2 9 

1953 

2078 

2203 

2327 

2452 

| 2676 

2701 

1 25 

349 

2825 2950 

8074 

3 i 99 

1 3323 

3447 

3571 

36 9 6 

j 3820 

3944 

124 

35 o 

544068 4192 

4316 

4440 

I 4564 

4688 

4812 

4 9 36 

! 5 o 6 o 

5 1 SoT 

124 

3 a i 

5307! 543 1 

5555 

5678 

! 58 o 2 

5925 

6049 

6172 

6296 

6419 

124 

352 

6043 

6666 

6789 

6913 

7 o 36 

7 i 5 9 

j 7282 

74o5 

7629 

7652 

123 

353 

7775 7898 

| 8021 

8144 

8267 

838 g 

85 i 2 

8635 

8758 

8881 

123 

354 

9003; 9126 

9249 

9371 

9494 

9616 

9739 

9861 

9984 

®io6 

123 

355 

550228 

o 35 i 

0473 

0595 

0717 

0840 

0962 

1084 

1206 

i 328 

122 

356 

1400 

1572 

1694 

1816 

1938 

2060 

2181 

23 o 3 

2425 

2547 

122 

357 

2663 

2790 

2911 

3 o 33 

3 1 55 

3276 

3398 

35 19 

364 o 

3762 

| 121 

353 

3883 

4004 

4126 

4247 

4368 

4489 

4610 

! 4731 

4852 

4973 

1 121 

309 

5094 

; 5215 

5336 

5467 

5578 

5699 

5820 

! 5940 

6061 

6182 

121 

36 o 

5563 o 3 

6423 

6544 

6664 

6785 

6 9 o 5 

7026 

7146 

7267 

7387 

120 

36 j 

7307 

: 7627 

7748 

7868 

7988 

8108 

8228 

834 9 

8469 

85 S 9 

120 

362 

8709 

8829 

8948 

9068 

9188 

9 3 o 8 

9428 

9548 

9667 

9787 

120 

363 

99 ° 7 

•©26 

•146 

®265 

®385 

® 5 o 4 

•624 

•743 

•863 

•982 

Il 9 

364 

56 x101 

1221 

i 34 o 

1469 

1578 

1698 

1817 

ig 36 

2 o 55 

2174 

119 

365 

2293 

2412 

253 1 

265 o 

2769 

2887 

3 oo 6 

3 1 2 5 

3244 

3362 

1 19 

366 

3481 

36 oo 

3 7 i 8 

3837 

3 9 55 

4074 

4192 

43 11 

4429 

4548 

II9 

367 

4666 

4784 

4903 

D02I 

5 139 

6257 

3376 

6494 

5612 

o ~] 3 o 

ll8 

363 

5848 

6966 

6084 

6202 

6320 

6437 

6555 

6673 

6791 

6909 

ll8 

369 

7026 

7144 

7262 

7379 

7497 

7614 

7732 

7S49 

7967 

8084 

I l8 

370 

568202 

83 19 

8436 

8554 

8671 

8788 

8 9 o 5 

9023 

g 1 4 o 

9257 

117 

3 7 1 

9874 

9491 

9608 

9725 

9842 

9969 

o® 7 6 

*i 9 3 

® 3 o 9 

•426 

I 17 

3 7 2 

570648 

0660 

0776 

0893 

1010 

1126 

1243 

1359 

1476 

i 5 9 2 

117 

376 

1709 

1826 

1942 

2 o 58 

2174 

229T 

2407 

2523 

2639 

2755 

I 10 

374 

2072 

2988 

3 104 

3220 

3336 

3432 

3568 

3684 

3800 

3915 

1 l6 

37a 

4 o 3 i 

4 U 7 

4263 

4379 

44 q 4 

46 lO 

4726 

4841 

49 5 7 

6072 

116 

376 

5 188 

53 o 3 

5419 

5534 

565 o 

0 -j 65 

588 o 

5 gg 6 

6111 

6226 

115 

3 77 

634 i 

6457 

6672 

6687 

6802 

6917 

7032 

7 r 47 

7262 

7377 

1 15 

3 ~]S 

7492 

7607 

7722 

7836 

79 5 i 

8966 

8181 

8296 

84 10 

8525 

1 15 

379 

8639 

8754 

8368 

8 9 83 

9°97 

9212 

9326 

9441 

9 555 

9669 

114 

3 . 8 o 

579784 

9898 : 

oo 1 2 

® 126 

®24l 

®355 

® 46 9 

•583 

•607 

•811 

114 

38 i 

580925 

1039 ; 

u 53 

1267 

i 38 i 

Uo 5 

1608 

1722 

1 836 

iq 5 o 

114 

332 

2063 

2177 

2291 

2404 

25 i 8 

263 1 

2745 

2858 

2972 

3 o 85 

114 

383 

3199 

3312 | 

3426 

3089 

3652 

3766 

3879 

3 99 2 

4 io 5 

4218 

113 

334 

433 1 

4444 i 

4557 

4670 

4733 

4896 

6009 

5 i 22 

5235 

5348 | 

11 3 

385 

0461 

55 7 4 

5686 

D799 

6912 

6024 

6137 

6280 

6362 

8475 

1 13 

386 

6587 

6700 

6812 

6926 

7037 

7149 

7262 

7374 I 

7486 

7999 

112 

3 o 7 

77 ii 

7323 ! 

7 9 3 d 

8047 

8160 

8272 

8384 

8496 

86 o 3 

8720 

112 

33 b 

8332 

8944 1 

9066 

9167 

9279 

9891 

9 5 o 3 

9 6 i 5 

9726 

9 838 

! J 2 

3 t >9 

9950 

*®6i 1 

*173 

*284 

©396 

® 5 o 7 1 

•619 

•730 j 

•842 

° 9 53 

113 

390 

591063 

1176 

1287 

1 3 99 

i 5 io 

1621 

1732 

1843 

1-955 

2066 

1 11 

891 

2177 

2288 I 

23 99 ' 

25 l 0 

2621 

2732 

2843 

2964 j 

3064 

3\-]5 

111 

3 o 2 

3286 

33 9 7 

35 o 8 

36 18 

3729 

3840 I 

3960 

4061 | 

4171 

4282 

111 

893 

4393 

45 o 3 1 

4614 

4724 

4834 

4946 

5 o 55 

5 i 65 

5276 

5386 

I 10 

894 

5496 

56 o 6 

5717 

6827 

5 9 37 

6047 

61 5 7 

6267 

6377 

6487 

110 

396 

6397 

6707 : 

6817 

^927 

7037 

7146 1 

7256 

7366 

7476 | 

7586 

I lO 

396 

7695 

7805 

7914 

8024 I 

81 34 j 

8243 

8353 j 

8462 J 

8572 I 

8681 

I 10 

397 

8791 

8900 

9009 

911*9 

9228 

9337 1 

9446 

9 556 

9 665 

9774 

I 09 

39 ^ 

9883 

999 2 

® 10 I 

G 2 1 0 

® 3 ig | 

® 42 » ! 

•537 

•646 

®755 

*864 

109 

499 

600973 

1082 

1191 

1299 i 

1408 

1 5 17 | 

1625 

1784 

1843 I 

i 9 5 i 

109 

N. 

1 

0 

1 

2 

3 

1 

4 

5 

6 

7 1 

8 

9 

D. 




















































































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 7 



N. 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 


4oo 

602060 

2169 

2277 

2386 

1494 

2603 

2711 

2819 

2928 

3o36 

108 


4oi 

3144 

3253 

3361 

3469 

3077 

3686 

3794 

3902 

4010 

4118 

108 


402 

4226 

4334 

4442 

455 o 

4658 

4766 

4874 

4982 

5089 

5197 

108 


4 o 3 

53o5 

54 i 3 

5521 

5628 

5 j 36 

5844 

5g5i 

6059 

6166 

6274 

108 


4o4 

63 81 

6489 

6096 

6704 

6811 

6919 

7026 

7133 

7241 

7348 

107 

1 

4oo 

7400 

7562 

7669 

7777 

7884 

7991 

8098 

82o5 

8312 

8419 

107 


406 

8026 

8633 

8740 

8847 

8954 

9061 

9 i6 7 

9274 

938 i 

9488 

107 


407 

9094 

9701 

9808 

9914 

®'®21 

®I28 

®234 

«34i 

•447 

■554 

107 


408 

61066c 

0767 

0873 

°979 

1086 

1192 

1298 

i 4 o 5 

151 x 

1617 

106 


409 

1723 

1829 

1936 

2042 

2148 

2264 

236o 

2466 

2572 

2678 

106 


4io 

612784 

2890 

2996 

3l02 

3207 

3313 

3419 

3525 

363o 

3736 

106 


411 

3842 

3 9 47 

4 o 53 

4 i 59 

4264 

4370 

4470 

458 i 

4686 

4792 

106 


412 

4897 

5oo3 

5 ig 8 

52i3 

53l9 

0424 

5529 

5634 

5740 

5845 

io5 


413 

5 g 5 o 

6o55 

6I60 

6265 

6370 

6476 

6581 

6686 

6790 

6896 

100 


4i4 

7000 

7106 

7210 

7315 

7420 

7023 

7629 

7734 

7889 

7943 

io5 


415 

8048 

8i 53 

8257 

8362 

8466 

8071 

8676 

8780 

8884 

8989 

io5 


416 

9093 

9198 

9802 

9406 

95ll 

9615 

9719 

9*24 

9928 

**32 

104 


417 

620186 

0240 

o344 

0448 

o 552 

o656 

0760 

0864 

0968 

1072 

104 


418 

1176 

12S0 

i 384 

1488 

1592 

1695 

1799 

1903 

2007 

2110 

104 


419 

2214 

23 i 8 

2421 

2520 

2628 

2782 

2835 

2939 

3o42 

3l46 

104 


420 

623249 

3353 

3406 

3559 

3663 

8766 

386 9 

3973 

4076 

4179 

io3 


421 

4282 

4385 

4488 

4591 

4695 

4798 

4901 

5 oo 4 

5107 

02 10 

io3 


422 

5312 

5415 

5518 

5621 

5724 

5827 

5929 

6082 

6135 

6238 

io3 


423 

634 o 

6443 

6546 

6648 

6751 

6853 

6966 

7068 

7161 

7263 

io3 


424 

7366 

7468 

7571 

7673 

777 5 

787S 

7980 

8082 

8x85 

8287 

102 


420 

8389 

8491 

85 9 3 

869O 

8797 

8900 

9002 

9104 

9206 

9308 

102 


426 

9410 

9512 

9613 

97i 5 

9817 

99 1 9 

®®2I 

® 123 

*224 

*326 

102 


427 

630428 

o53o 

o63i 

0733 

o835 

0986 

io38 

1139 

1241 

X 342 

102 


428 

1444 

1545 

1647 

1748 

1849 

19D1 

2052 

2153 

2 200 

2356 

I0i 


429 

2407 

2559 

2660 

2761 

2862 

2963 

3064 

3165 

3 266 

3367 

IOl j 


43o 

633468 

3569 

3670 

377 1 

38 7 2 

3 97 3 

4074 

4170 

4276 

4376 

100 


431 

4477 

4078 

4679 

4779 

4880 

4981 

5o8i 

5182 

5283 

5383 

100 


432 

5484 

5584 

5685 

6786 

5886 

6986 

6087 

6187 

6287 

6388 

100 


433 

6488 

6588 

6688 

6789 

6889 

6989 

7089 

7 i8 9 

7290 

7890 

100 


434 

7490 

709° 

7690 

7790 

7890 

7990 

8090 

8190 

8290 

8889 

99 


435 

8489 

8589 

8689 

8789 

8888 

8988 

908S 

9188 

9287 

9887 

99 


436 

9486 

9686 

9686 

9780 

9880 

9984 

®®84 

®r83 

®283 

*382 

99; 


437 

640481 

o58i 

0680 

°779 

0879 

0978 

1077 

1177 

1276 

\ 3-]5 

99 


438 

1474 

1578 

1672 

1771 

1871 

1970 

2069 

2168 

2267 

2366 

99 


439 

2460 

2563 

2662 

2761 

2860 

2959 

3o58 

3156 

3255 

3354 

99 


44o 

643453 

355i 

365o 

3749 

3847 

3946 

4044 

4i43 

4242 

434o 

98! 


441 

4439 

4537 

4636 

4734 

4832 

4931 

6029 

5127 

6226 

5324 

98 


442 

5422 

5521 

6619 

5717 

58i5 

6913 

6011 

6110 

6208 

6 3 06 

9 S . 


443 

6404 

65o2 

6600 

6698 

6796 

6894 

6992 

7089 

I‘ 8 I 

7280 

98 


444 

73S3 

7481 

7079 

7676 

7774 

7872 

7969 

8067 

8160 

8262 

98 


443 

836o 

8408 

8555 

8653 

8760 

8848 

8945 

904.3 

9140 

9237 

97 


446 

o335 9432 

953c 

9627 

9724 

9821 

99 1 9 

•® 16 

®n3 

®2 10 

97 i 

J 

447 

65o3o8 

0406 

g 5 o 2 

0699 

0696 

0793 

0890 

0987 

1084 

I l8l 

971 

\ 

443 

1278 

1370 

U72 

1069 

1666 

1762 

1809 

1966 

2 o 53 

2i5o 

97 


449 

2246 

2343 

2440 

2536 

2633 

2 j 3 o 

2826 

2923 

3019 

3116 

97 j 


45 o 

6532i3 

33o9 

34o5 

35 o 2 

3598 

3695 

3791 

3888 

3984 

408c 

96, 
961 


401 

4577 

4278 

4369 

4465 

4562 

4658 

4704 

4800 

4946 

5 o 42 


462 

5138 

5235 

5331 

0427 

5523 

56i 9 

07*15 

5810 

0906 

6002 

9.6! 

96 j 


453 

6098 

6194 

6290 

6336 

6482 

6077 

6673 

6769 

6864 

6960 


4.54 

7006 

7162 

7247 

7343 

7438 

7534 

7629 

7720 

7820 

7916 

96; 

* 

455 

8011 

8107 

8202 

8298 

83g3 

8488 

8584 

8679 

8774 

8870 

90J 

1 

436 

8960 

9060 

9i55 

9200 

9346 

9441 

9536 

9681 

9726 

9821 

9 :>j 

1 

467 

9916 

«®ii 

e io6 

°20I 

*296 

®39i 

®486 

*081 

*676 

® 77 , 

90 


456 

660860 

0960 

io55 

i i5o 

1240 

x 339 

1434 

1629 

1623 

1718 


l 


i8i3 

1907 

2002 

2096 

2191 

2286 

238 o 

2470 

2069 

2663 

90 j 

' . 

T+T 

IN. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 j 

1 

i i -9 





















































































B 


A TABLE OF LOGARITHMS FROM 1 TO 10,000 


N. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D. 

460 

662758 

2852 

2947 

3 o 4 i 

3 1 35 

323 o 

3324 

3418 

35 i 2 

3607 

94 

461 

3701 

3790 

3889 

3 9 S 3 

4078 

4172 

4266 

436 o 

4454 

4548 

94 

462 

4642! 

4706 

483 o 

4924 

5 oi 8 

5 112 

6206 

5299 

5393 

5487 

94 

463 

558 1 

5675 

5769 

5862 

5956 

6 o 5 o 

6143 

6287 

633 1 

6424 

94 

464 

65 8 

6612 

6706 

6799 

6892 

6986 

7079 

7173 

7266 

7360 

94 

1 465 

7453 

7546 

7640 

7733 

7826 

792c 

801 3 

8106 

8199 

8293 

98 

! 466 

8386 

8479 

8572 

8665 

8709 

8832 

8945 

9088 

91 3 1 

9224 

98 

i 467 

9817 

9410 

g 5 o 3 

9596 

9689 

9782 

9873 


•®6o 

*i 53 

98 

; 46 « 

670246 

0339 

043 1 * 

0024 

0617 

0710 

0802 

0896 

0988 

1080 

98 

1 469 

11731 

1265 

i 358 

1401 

1 543 

i 636 

1728 

1821 

1913 

2005 

98 

! 470 

672098, 

2190 

2283 

2375 

2467 

256 o 

2652 

2744 

2836 

29^9 

92 

1 ' 
t 47 1 

3021 

3 i i 3 

32 o 5 

3297 

3390 

3482 

3574 

3666 

3758 

385 o 

92 

1 * 

* 472 

3942 

4034 

4126 

4218 

43 10 

4402 

4494 

4586 

4677 

4769 

92 

473 

4861 

4953 

5 o 45 

5)37 

5228 

5320 

5412 

55 o 3 

5596 

5687 

92 

474 

6778 

5870 

5962 

6 o 53 

6145 

6236 

6328 

6419 

65 i 1 

6602 

92 

47 5 

6694 

6785 

6876 

6068 

7069 

71 5 1 

7242 

7333 

7424 

7516 

9 1 

? 476 

7607 

7698 

7789 

7881 

T 972 

8 o 63 

81 54 

8245 

8336 

8427 

9 1 

477 

85 18 

8609 

8700 

8791 

8882 

8973 

9064 

9100 

9246 

9887 

9 1 

478 

9428 

9 3l 9 

9610 

9700 

979 1 

9882 

9973 

e ®63 

®i54 

•245 

9 1 

479 

68 o 336 

0426 

0617 

0607 

0698 

0789 

0879 

0970 

1060 

1 15 1 

9 i 

; 430 

681241 

1 332 

1422 

1 5 1 3 

i 6 o 3 

1693 

1784 

1874 

1964 

2055 

90 

! 431 

2140 

2235 

2826 

2416 

25o6 

2596 

26S6 

2777 

2867 

29?7 

90 

; 482 

3o47 

3 137 

3227 

3317 

3407 

3497 

3587 

36 7 7 

3767 

3807 

90 

483 

3947 

4037 

4127 

4217 

4307 

4396 

4486 

4576 

4666 

4756 

90 

484 

4845 

4935 

5o23 

0114 

5204 

6294 

5383 

5473 

5563 

5652 

oo 

i 485 

5742 

5 « 3 i 

5921 

6010 

6100 

6189 

6279 

6368 

6458 

6547 

89 

} 486 

6636 

6726 

68 i 5 

6904 

6994 

7 o 83 

7172 

7261 

735i 

7440 

89 

i 487 

7629 

7618 

7707 

7796 

7886 

7973 

8064 

81 53 

8242 

833 1 

89 

i 488 

8420 

8509 

8098 

6687 

8776 

8865 

8953 

9042 

91 3 1 

Q220 

89 

489 

9309 

9398 

9486 

9073 

9664 

9753 

9841 

9930 

*•19 

*107 

89 

490 

690196 

0285 

o 373 

0462 

o 55 o 

o 63 y 

0728 

0816 

0905 

0993 

89 

491 

y io$i 

1170 

1258 

1 347 

1435 

i524 

1612 

1700 

1789 

1877 

88 

492 

1965 

2o53 

2142 

2230 

23 18 

2406 

2494 

2083 ,| 

2671 

2709 

88 

4 9 3 

2847 

2935 

3023 

3hi 

3*99 

3287 

3375 

3463 

355 1 * 

3639 

88 

494 

3727 

38j5 

3903 

3991 

4078 

4i66 

4254 

4342 

443o 

45 i 7 

88 

495 

4600 

4693 

4781 

4868 

4906 

5o44 

5 i 3 1 

5219 

53o7 

5394 

88 

496 

5482 

556c; 

5657 

5744 

5832 

6919 

6007 

6094 

6182 

6269 

87 

497 

6356 

6444 

653 1 

6018 

6706 

6798 

68S0 

6968 

7o55 

7142 

87 

498 

7229 

7817 

7404 

7491 

7378 

7665 

7762 

7839 

7926 

8014 

87 

499 

8101 

8188 

8275 

8362 

8449 

8535 

8622 

8709 

8796 

8883 

87 

000 

608970 

9067 

9144 

923) 

9317 

94 o 4 

9491 

9 5 7 8 

9664 

975i 

87 

5 oi 

9 838 

9924 


»® 9 S 

•184 

•271 

*358 

•444 

• 53 i 

•617 

87 

502 

700704 

0790 

0877 

0963 

io 5 o 

1 1 36 

1222 

1 309 

1395 

1482 

• 86 

5 o 3 

1 568 

1604 

1741 

1827 

1913 

1999 

2086 

2172 

2258 

2344 

86 

5 o 4 

243i 

2617 

26 o 3 

2689 

2770 

2861 

2947 

3 o 33 

3i 19 

32o5 

86 

5 o 5 

3291 

3377 

3463 

3549 

3635 

3721 

3807 

389.3 

3979 

4o65 

86 

5 o 6 

4101 

4236 

4322 

4408 

4494 

4579 

4665 

4701 

483 7 

4922 

86 

5 o~i 

5 ooS 

6094 

5179 

5265 

535 o 

5436 

5522 

5607 

5693 

5 77 8 

86 

5 o 8 

5864 

5949 

603.0 

6120 

6206 

6291 

6376 

6462 

6547 

6632 

85 

609 

6718 

68 o 3 

6888 

6974 

7059 

7144 

7229 

73i 5 

74oo 

7485 

85 

5 io 

707570 

7655 

7740 

7826 

7911 

7996 

8081 

8166 

825 i 

8336 

85 

5 i 1 

8421 

85 o 6 

8691 

8676 

8761 

8846 

8931 

9016 

9100 

9185 

85 

5 12 

9270 

9355 

9440 

9524 

9609 

9694 

9779 

9863 

9948 

«®33 

85 

5 i 3 

710117 

0202 

0287 

0371 

0456 

0040 

0625 

0710 

0794 

0879 

85 

DI 4 

0960 

1048 

1132 

i 1217 

i 3 oi 

1 385 

1470 

1 554 

1609 

1723 

84 

515 

1807 

1892 

1976 

i 2060 

2144 

2229' 

23 1 3 

2397 

I 2481 

2066 

84 

5 i 6 

265o 

2734 

I 2818 

1 2902 

2986 

3070 

3 1 54 

3238 

3323 

3407 

84 

1 5i7 

! 3491 

3070 

| 8609 

| 8742 

3826 

3910 

3994 

| 4078 

4162 

4246 

84 

} 5 i 8 

433 ci 

44 i 4 

4 497 

458 1 

4665 

4749 

4833 

4916 

5 ooo 

5084 

84 

1 5i9 

j 5167 

1 525 ) 

1 

5335 

54)8 

j 55 o2 

! 5586 

6669 

5753 

1 

5836 

5920 

84 

: N. 

» 

0 

1 

i 

2 

3 

4 

I 5 

! 6 

l 

! *» 

8 

1 9 

D. 


































































































A TABLE OF LOGARITHMS FROM 1 TO 10 . 000 . 

t 


9 


N. 

0 

I 

2 

3 

4 

5 

6 

7 1 

8 

] 

9 

JD. 

520 

716003 

6087 

6170 

6254 

633 7 

6421 

65 o 4 

6588 

6671 

6754 

83 

521 

6838 

6921 

7004 

7088 


7254 

7338 

7421 

7004 

7 58 7 

83 

522 

7671 

7754 

7837 

7920 

8 oo 3 

8086 

8169 

8253 

8336 

8419 

83 

523 

8502 

8585 

8668 

8761 

8834 

89*7 

9000 

9083 | 

9165 

9248 

83 

524 

9 33 r 

9414 

9497 

9580 

9663 

9745 

9828 

99 I 1 , 

9994 

*®77 

83 

520 

720169 

0242 j 

0825 

0407 

0490 

0673 

o 655 

0738 1 

0821 

0903 

83 1 

526 

0986 

1068 

11 5 1 

1233 

1 3 16 

1 3 9 8 

1481 

1 563 

1646 | 

1728 

82 

527 

1811 

1893 

1975 

2 o 58 

2140 

2222 

23 o 5 

2387 

2469 

2552 

82 

528 

2634 

2716 

2798 

2881 

2963 

3 o 45 

3127 

3209 1 

3291 1 

3374 

82 

529 

3456 

3538 

3620 

3702 

3784 

3866 

3948 

4 o 3 o | 

4112 

4194 J 

82! 

53 o 

724276 

4358 

4440 

4522 

4604 

4685 

4767 

4849 j 

493 i 

5 oi 3 

82 

53 1 

6095 

6176 

5258 

5340 

5422 

55 o 3 

5585 

6667 

5748 

583 o 

82 | 

532 

6912 

6993 

6075 

6 i 56 

6238 

6320 

6401 

6483 ] 

6564 

6646 

82 I 

533 

6727 

6809 

6890 

6972 

7 o 53 

7 i3 4 

7216 

7‘297 i 

7379 

7460 

81 

534 

7641 

7623 

7704 

7780 

7866 

7948 

8029 

8(io 

8191 

8273 

81 

535 

8354 

8435 

85 j 6 

85 9 7 

8678 

8769 

8841 

8922 

9003 

9084 

81 ! 

536 

91 65 

9246 

9327 

9408 

9489 

907° 

965 i 

9732 

9818 

9893 

81 

537 

9974 

**55 

w 1 36 

*217 

•298 

® 3 7 8 

*459 

®04o 

*621 

*702 

81 

538 

730782 

o 863 

0944 

1024 

1 ioo 

1186 

1266 

1 347 

1428 

i 5 o 8 

81 

53 9 

1689 

1669 

1750 

i 83 o 

1911 

1991 

2072 

2152 

2233 

23(3 

81 

54 o 

732394 

2474 

2555 

2635 

2715 

2796 

2876 

2906 

3 o 37 

3117 

So 

54 i 

3197 

3278 

3358 

3438 

35 18 

3598 

36 79 

3709 

3889 

39(9 

80! 

542 

3999 

4079 

4160 

4240 

4320 

4400 

4480 

4560 

4640 

4720 

8° 

543 

4800 

4880 

4960 

5 040 

5 l 20 

5200 

6279 

5359 

5439 

55 19 

801 

544 

5599 

6679 

0709 

5838 

5 gi 8 

5998 

6078 

6157 

6287 

63(7 

80 

546 

6397 

6476 

6556 

6635 

6715 

6795 

6874 

6954 

7034 

7113 

80 

546 

7193 

7272 

7352 

7431 

7511 

7590 

7670 

7749 

7829 

7908 

79 

047 

7987 

8067 

8146 

8226 

83 o 5 

8384 

8463 

8^)43 

8622 

8701 

79 

548 

8781 

8860 

8 q 3 q 

9018 

9°97 

9 1 77 * 

9256 

9880 

9414 

9493 

79 

549 

9572 

965 i 

9731 

9810 

9889 

9968 

°*47 

*126 

® 2 o 5 

*284 

79 

55 o 

74 o 363 

0442 

0521 

0600 

0678 

0757 

o 836 

0915 

0994 

1073 

79 

55 i 

I 152 

I 23 o 

1309 

1388 

1467 

i 54.6 

1624 

1703 

1782 

i860 

79 

552 

iq 3 q 

2018 

2096 

2175 

2254 

2332 

2411 

2489 

2568 

2647 

79 

553 

2726 

2804 

2882 

2q6i 

3 o 39 

3 u 8 

3196 

3275 

3353 

343 i 

78 

554 

35 io 

3588 

0667 

3745 

3823 

3902 

3 9 8 o 

4 o 58 

41 36 

421 5 

78 

555 

42 q 3 

4371 

4449 

4528 

4606 

4684 

4762 

4840 

4919 

4997 

78 

556 

Soto 

5 i 53 

523 1 

53 o 9 

5387 

5465 

5543 

5621 

5699 

5777 

78 

557 

5855 

5 9 33 

6011 

6089 

6167 

6245 

6323 

6401 

6479 

6556 

78 

558 

6634 

6712 

6790 

6868 

6945 

7023 

7101 

7 1 79 

7256 

7334 

78 

559 

7412 

7489 

7667 

7645 

7722 

7800 

7878 

7900 

8 o 83 

8110 

78 

56 o 

748188 

8266 

8343 

8421 

84.98 

8676 

8653 

8781 

8808 

I 8885 

77 

56 1 

‘ 8 9 63 

9040 

9118 

9190 

9272 

935 o 

9427 

9604 

9682 

9669 

77 

" 562 

9786 

9814 

9891 

996b 

®*»40 

°I 23 

®200 

©277 

*354 

e 43 i 

77 

563 

700008 

o 586 

o 663 

0740 

0817 

0894 

O97I 

1048 

I I 25 

j 202 

77 

56 4 

I 2*70 

1 356 

1433 

i 5 io 

1587 

1664 

1741 

1818 

1890 

1972 

77 

565 

2048 

2125 

2202 

2279 

2356 

2433 

2609 

2586 

2663 

2740 

77 

566 

2816 

2893 

2970 

3 o 47 

3 1 23 

3200 

3277 

33 o 3 

343 o 

35 o 6 

77 

567 

3583 

366 o 

3-/36 

38 x 3 

3889 

8966 

4042 

4119 

4 Hp 

4272 

! 77 

568 

4848 

4425 

45 oi 

4678 

4654 

4730 

4807 

4883 

4960 

5 o 36 

70 

D69 

5 i 12 

5 i 8 9 

5265 

5341 

5417 

0494 

OO7O 

5646 

5722 

0799 

: 70 ; 

5 ~jo 

755875 

D 95 l 

6027 

6 io 3 

6180 

6256 

6332 

6408 

6484 

6060 


5 ii 

6636 

6712 

6788 

6864 

6940 

7016 

7092 

7168 

7244 

7320 

76 

572 

7806 

7472 

7648 

7624 

7700 

777 3 

7861 

7927 

8 oo 3 

! 8079 

7 6 

573 

Si 55 

823 o 

83 06 

8382 

8458 

8533 

8609 

8685 

8761 

; 8836 

1 i: 

574 

8912 

8988 

9063 

9 l3 9 

9214 

9290 

9366 

944 * 

1 9017 

9092 

76 

i 577 

9668 

9743 

9819 

9894 

9970 

®» 4 o 

® 121 

*196 

*272 

*347 

1 "8 j 

! 576 

fn 7 

760422 

I I 7 6 

| 0498 

1201 

0673 
i 326 

0649 

1402 

0724 

1477 

0799 

(002 

0876 

1627 

0900 

1702 

1025 

1 1778 

11 or 

, 1 853 

1 70 
: 75 

j 5 7 !i 

! & 7 Q 

J 7 

1928 

2679 

2003 

2754 

2078 

2829 

21 53 
2904 

2228 
j 2978 

23 o 3 

3 o 53 

2378 

3(23 

2453 

32 o 3 

1 2529 

I 3278 

2604 
| 3353 

! ’5 

i n - 

i. —- 

0 

. 

i 2 

3 

4 

5 

6 

7 

8 

9 



( 
























































































10 


A TABLE OF LOGARITHMS FROM L TO 10,000 




N. 

0 

1 

2 

3 

4 

5 


7 

8 

9 

P- 

58o 

763428 

35o3 

3578 

3653 

3727 

3802 

3877 

3962 

4027 

4101 

73 

581 

4176 

4231 

4326 

44oo 

4475 

4330 

4624 

4699 

4774 

484S 

75 

582 

4923 

4998 

0072 

5147 

5221 

5296 

5370 

5445 

5520 

3594 

73 

583 

0669 

5743 

5818 

5892 

6966 

6041 

6115 

6190 

6264 

6338 

74 

584 

6413 

6487 

6062 

6636 

67IO 

6786 

6889 

6933 

7007 

7082 

74 

585 

7156 7280 

73o4 

7379 

7453 

7327 

7601 

7673 

7749 

: ? 2j 

74 

586 

7898 

7972 

8046 

8120 

8194 

8268 

8342 

8416 

8490 

8364 

74 

0S7 

8638 

8712 

8786 

8S60 

8934 

9008 

9082 

9166 

9280 

cc’o3 

74 

588 

9377 

9451 

9620 

9699 

9673 

9746 

9820 

989^ 

9968 

*•42 

74 

689 

7701i5 

0189 

0263 

o336 

0410 

0484 

0537 

o63i 

0705 

0778 

74 

590 

77oS52 

0926 

0999 

1073 

1 146 

1220 

1293 

1367 

1440 

i5i£ 

74 

691 

i53 7 

1661 

1734 

1808 

l88l 

1955 

2028 

2102 

2175 

2248 

7 o 

O92 

2322 

23g5 

2468 

2542 

26l5 

2688 

2762 

2S35 

2908 

2981 

73 

5 9 3 

3o55 

3128 

3201 

3274 

3348 

3421 

3494 

3567 

3640 

3713 

73 

694 

3786 

386o 

3 9 33 

4006 

4079 

4l32 

4225 

4298 

4371 

4444 

73 

69:3 

4517 

4590 

4663 

47^6 

4809 

4882 

4933 

5o28 

3100 

3173 

7 3 

696 

8246 

5319 

5392 

5465 

5538 

5610 

3683 

5 7 56 

5829 

6902 

73 

697 

6974 

6047 

6120 

6193 

6265 

6338 

6411 

6483 

6550 

6629 

73 

5,S 

670. 

6774 

6846 

6919 

6992 

7064 

7137 

7209 

7282 

7354 

73 

C>99 

7427 

7499 

7572 

7644 

7717 

7789 

7862 

7934 

8006 

8079 

72 

O' 

0 

0 

778l5l 

8224 

8296 

8368 

8441 

8513 

8585 

8658 

8730 

8802 

72 

601 

8874 

8947 

9019 

9091 

9i63 

9236 

93oS 

9380 

9432 

9624 

72 

602 

9696 

9669 

974i 

9813 

9886 

9937 

<**29 

®10I 

*173 

®243 

72 

6o3 

780317 

0889 

0461 

o533 

060 5 

0677 

0749 

0821 

0893 

0966 

72 

604 

1037 

1109 

1181 

1253 

1324 

1396 

1468 

1540 

1612 

1084 

72 

6o5 

i 7 55 

1827 

1S99 

1971 

2042 

2114 

2186 

2258 

2329 

2401 

72 

606 

2473 

2544 

2616 

2688 

2739 

283i 

2902 

2974 

3 046 

3117 

72 

607 

3189 

3260 

3332 

34o3 

3475 

3546 

3618 

368q 

3761 

3832 

1* 

608 

3904 

3975 

4046 

4118 

4189 

4261 

4332 

44o3 

4475 

4546 

7* 

609 

4617 

4689 

4760 

4831 

4902 

4974 

5o45 

5i 16 

6187 

5269 

7i 

610 

78533o 

5401 

5472 

5543 

5615 

5686 

5 7 57 

5828 

5899 

0970 

7i 

611 

6041 

6112 

6183 

6254 

6323 

63g6 

0467 

6538 

6609 

6680 

7i 

612 

6 -] 5 i 

6822 . 

6893 

6964 

7035 

7106 

7177 

724S 

73i 9 

73 9 o 

7 1 

613 

7460 

753i 

7602 

7673 

7744 

7813 

7883 

7 9 56 

8027 

8098 

7i 

614 . 

8168 

8289 

8310 

8381 

8451 

8522 

8393 

8663 

8734 

8804 

7i 

615 

8870 

8946 

9016 

9087 

9157 

9228 

9299 

9369 

9440 

9010 

7i 

616 

9581 

965i 

9722 

9792 

9863 

qq33 


*<* 7 4 

®i44 

®2I3 

70 

617 

790286 

o356 

0426 

0496 

0367 

0637 

0707 

0778 

0848 

0918 

70 

618 

0988 

1059 

1129 

1199 

1269 

1340 

1410 

1480 

1330 

1620 

70 

619 

1691 

1761 

1831 

1901 

1971 

2041 

2111 

2181 

2252 

2322 

7° 

620 

792802 

2462 

2532 

2602 

2672 

2742 

2812 

2882 

2952 

3022 

70 

621 

3092 

3i62 

3231 

33oi 

3371 

3441 

3511 

358i 

365i 

3721 

70 

622 

3790 

386o 

3930 

4000 

4070 

4i39 

4209 

4279 

4349 

44 

70 

623 

4488 

455S 

4627 

4697 

4767 

4836 

4906 

4976 

5043 

5i i5 

70 

624 

5185 

5254 

5324 

53 9 3 

5463 

5532 

3602 

5672 

3741 

53n 

70 

025 

538o 

0949 

6019 

6088 

6158 

6227 

6297 

6366 

6436 

65g5 

69 

620 

6574 

6644 

6713 

6782 

6852 

6921 

6990 

7060 

7129 

7198 

69 

627 

7268 

7337 

7406 

7475 

75/(5 

7614 

7683 

7732 

7821 

7890 

69 

628 

7960 

8029 

8098 

8167 

8236 

83o5 

83 7 4 

8443 

85i3 

8582 

69 

629 

8651 

8720 

8789 

8858 

8927 

8996 

9066 

9i34 

9203 

9272 

69 

63o 

799341 

9409 

9478 

9547 

9616 

9 685 

9754 

9823 

9892 

9961 

69 

631 

800029 

0098 

0167 

0236 

o3o5 

0878 

0442 

o5i 1 

o53c 

0648 

69 

632- 

0717 

0786 

o854 

0923 

0992 

1061 

1129 

1198 

1266 

i335 

69 

l 633 

1404 

1472 

1541 

1609 

1678 

1747 

1 Si 5 

1384 

1962 

2021 

69 

634 

2089 

2158 

2226 

2290 

2363 

2432 

2300 

2568 

2637 

270? 

6q 

635 

2774 

2842 

2910 

2979 

3o47 

3116 

3184 

3232 

3321 

3389 

63 

636 

3457 

3525 

3594 

3662 

3 - j 2 o 

3798 

3867 

3983 

( 4°o3 

4071 

68 

637 

4139 

4208 

4276 

4344 

4412 

4480 

4548 

4616 

4685 

4753 

68 

638 

4821 

4889 

4907 

3025 

5093 

5161 

3229 

5297 

5365 

5/(33 

68 

| ^39 

55oi 

3369 

363 7 

3705 

5 77 3 

584i 

6908 

D976 

6044 

6112 

68 

i N - 

0 

1 

2 

3 

4 

I 5 

6 

7 

8 

9 

I). 






















































































A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


11 


N. 

i 0 

! 

j I 

2 

3 

4 

5 

1 6 

i 7 

8 

9 

p 

640 

! 806180 

6248 

63 16 

6384 

645 1 

65 19 

6687 

6655 

6723 

6790 

68 

641 

6858 

6926 

6994 

7061 

7129 

7 i 97 

] 7264 

( 7332 

74 oo 

7467 

68 

642 

7535 

7603 

7670 

77 38 

7806 

7873 

7941 

8008 

8076 

8143 

68 

643 

8211 

8279 

8346 

« 4 i 4 

8481 

8549 

8616 

8684 

8761 

8818 

67 

644 

8886 

8953 

9021 

9088 

9 i 56 

9228 

9 2 9 ° 

9358 

9426 

9492 

67 

645 

9660 

9627 

9694 

9762 

9829 

9896 

9964 

®® 3 1 

, *®98 

°i6o 

67 

646 

8 io 233 

o 3 oo 

0367 

043 /p 

o 5 oi 

0669 

o 036 

0703 

0770 

0837 

67 

647 

; 0904 

0971 

. lo3 9 

1106 

1173 

i 1240 

I i 3 o 7 

1874 

1441 

x 5 o 8 

67 

648 

107 0 

1642 

1709 

1776 

i 843 

1910 

1977 

2044 

2111 

2178 

67 

649 

2245 

23 12 

2379 

2440 

25 12 

2679 

2646 

2718 

2780 

2847 

67 

65 o 

812913 

2980 

3047 

3 114 

3 1 8t 

3247 

! 33 14 

338 1 

3448 

35 14 

67 

65 1 

, 358 1 

3648 

3714 

3781 

3848 

3914 

3981 

4048 

41 x 4 

4181 

67 

652 

4248 

43 1 4 

438 1 

4447 

4014 

458 1 

. 4647 

4714 

4780 

4847 

67 

608 

4913 

4980 

6046 

5 1 13 

5 i 79 

6246 

: 5312 

0378 

5445 

55 11 

66 

654 

5578 

5644 

6711 

5777 

5843 

5910 

5976 

6042 

6109 

6175 

66 

655 

6241 

63 o 8 

6374 

6440 

65 o 6 

6073 

6639 

6706 

6771 

6838 

66 

656 

6904 

6970 

7036 

7102 

7169 

7280 

73 oi 

7867 

7433 

7499 

66 

65 ~i 

7565 

7681 

7698 

7764 

7830 

7896 

7962 

8028 

8094 

8100 

66 

658 

8226 

8292 

83 08 

8424 

8490 

8556 

8622 

8688 

8754 

8820 

66 

659 

8885 

8961 

9017 

9083 

9149 

921 5 

9281 

9346 

9412 

9478 

66 

660 

819644 

9610 

9676 

9741 

9807 

9873 

99 3 9 

®*®4 

GO70 

®i 36 

66 

661 

820201 

0267 

o 333 

0399 

0464 

o 53 o 

0O9O 

0661 

0727 

0792 

66 

662 

o 858 

0924 

0989 

1000 

1120 

1186 

x 201 

1 3 17 

1 382 

1448 

66 

663 

1 5 14 

1 679 

i 645 

1710 

1770 

1841 

1906 

1972 

2087 

2 io 3 

65 

664 

2168 

2233 

2299 

2864 

2480 

2490 

2660 

2626 

2691 

2766 

65 

665 

2822 

2887 

2962 

3 ox 8 

3 o 83 

3148 

3 21 3 

3279 

3344 

3409 

65 

666 

3474 

3539 

36 o 5 

3670 

3735 

38 oo 

3865 

8980 

3996 

4061 

65 

667 

4126 

4191 

4256 

4321 

4386 

4401 

45 16 

4081 

4646 

47IX 

65 

668 

4776 

4841 

4906 

497 1 

5 o 36 

5 ioi 

5 i 66 

6281 

5296 

536 i 

65 

669 

0426 

5491 

5556 

5021 

5686 

5 ’] 5 i 

58 i 5 

588 o 

8940 

6010 

65 

670 

826075 

6140 

6204 

6269 

6334 

6399 

6464 

6523 

6693 

6658 

65 

671 

6723 

6787 

6852 

6917 

6981 

7046 

Vi 1 

7170 

7240 

73 o 5 

65 

672 

7869 

7434 

7499 

7063 

7628 

7692 

1V1 

7821 

7886 

79 5 i 

65 

67 3 

801 5 

8080 

8144 

8209 

8273 

8338 

8402 

8467 

853 1 

8095 

64 

' 674 

8660 

8724 

8789 

8853 

8918 

8982 

9046 

9111 

9170 

9289 

64 

678 

93 o 4 

9368 

9432 

9497 

9661 

9626 

9690 

9754 

9818 

9882 

64 

676 

9947 

e<s l 1 

®»7 5 

*189 

°204 

*268 

*332 

*896 

®46o 

^525 

64 

677 

830089 

o 653 

0717 

0781 

0845 

0909 

0978 

1087 

X 102 

1166 

64 

678 

123 o 

1294 

i 358 

1422 

i486 

1000 

161 4 

1678 

1742 

1806 

64 

679 

1870! 

1934 

1998 

2062 

2126 

2189 

2253 

2317 

23 Si 

2440 

64 

680 

832609 

2673 

2637 

2700 

2764 

2828 

2892 

2906 

3020 

3 o 83 

64 

681 

3147! 

3211 

3275 

3338 

3402 

3466 

3530 

35 9 3 

3657 

3721 

64 

682 

3784I 

3848 

3912 

3975 

4 o 39 

4 io 3 

4x66 

4280 

4294 

4357 

64 

683 

442 i| 

4484 

4548 

4611 

4676 

4789 

4802 

4866 

4929 

4998 

64 

684 

5 o 56 j 

6120 

5 i 83 

5247 

53 10 

53 "7 3 

5437 

0000 

5564 

5627 

63 

685 

5691 j 

0754 

0817 

588 1 

5944 

6007 

6071 

61 34 

6197 

6261 

63 

686 

. 6324 ! 

6887 

645 1 

6014 

6077 

6641 

6704 

6767 

683 o 

6.894 

63 

687 

6967 

7020 

7083 

7146 

7210 

7273 

7886 

7399 

7462 

7620 

63 

688 

7688 

7662 

77 x 5 

7773 

7341 

79°4 

7967 

8080 

8093 

81 56 

63 

689 

8219 

8282 | 

8345 

8408 

8471 

8534 

8697 

8660 

8723 

8786 

63 

69° | 

838849 

8912 

8975 

9038 

9101 i 

9164 

9 2 ?7 

9280 

9352 

941 5 

63 

69 1 

9478 

9541 1 

9604 | 

9667 

9729 

979 2 

9800 

9918 

9981 

*®43 

63 

692 

840106 

0169 

0232 j 

0294 

0867 I 

0420 

0482 

0045 

0608 

067 x 

63 

6 q 3 I 

0733 

0796 

0869 1 

0921 

0984 

1046 

1109 

1172 

1234 

1297 

63 

694 i 

1359 

1422 

1480 

1047 

1610 

1672 

1735 

1797 

i860 

1922 

63 

696 j 

1985 

2047 

2IIO 1 

2172 j 

2 235 j 

2297 

236 o 

2422 

2484 

2547 

621 

696 | 

2609 

2672 

2734 

2796 1 

2869 

2921 

2983 

3 o 46 

3 xo 8 

3170 

62 

697 

3233 

3296 

3357 

3420 

3482 

3544 

36 o 6 

3669 

373 i 

8798 

621 

698 

3855 

3 q 1 8 j 

39S0 

4042 j 

4104 

4166 

4229 

4291 

4353 

4415 

62 

699 J 

4477 ; 

4^9 I 

460l 

4664 

1 

4726 

4788 

485 o 

49x2 

4974 

5 o 36 

61 1 

N. ; 

1 

C i 

1 

, 

2 

3 i 

4 

5 

6 

7 

8 '] 

9 

i ) 



























































































L2 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

0 

I 

2 

3 

4 

5 

6 

7 

8 

9 

i>. 

100 

843098 

5i6o 

5222 

5284 

5346 

5408 

5470 

5532 

5394 

5656 

62 

701 

5 7 18 

5780 

5842 

5904 

5966 

6028 

6090 

6151 

6213 

6276 

82 

702 

633 t 

6399 

6461 

6523 

6585 

6646 

6708 

6770 

6832 

6894 

62 

703 

6935 

7017 

7°79 

7*41 

7202 

7264 

7826 

7388 

7449 

7011 

62 

704 

7373 

7634 

7696 

‘ 7758 

7819 

7881 

7943 

8004 

8066 

8128 

62 

7o5 

8189 

8231 

83i2 

8374 

8435 

8497 

8559 

8620 

8682 

8743 

62 

706 

8803 

8866 

8928 

8989 

9 o 5 i 

9112 

9174 

9235 

9297 

9 358 

6i 

7°7 

9419 

9481 

9342 

9604 

9666 

9726 

9788 

9849 

9911 

9972 

61 

708 

85oo33 

0095 

0156 

0217 

0279 

o 34 o 

040 * 

0462 

0324 

0080 

61 

709 

0646 

0707 

0769 

o83o 

0891 

0962 

ioj 4 

1075 

1136 

* *97 

61 

710 

85i258 

1320 

i38i 

1442 

i5o3 

1564 

i 625 

1686 

*747 

1809 

61 

711 

1870 

1 g31 

1992 

2053 

2114 

2173 

2236 

2297 

2358 

24*9 

61 

712 

2480 

2041 

2602 

2663 

2724 

2783 

2846 

2907 

2968 

3029 

61 

7i3 

3090 

3i5o 

3211 

3272 

3333 

3394 

3455 

3516 

3377 

3637 

61 

7*4 

36 9 8 

3759 

3820 

3881 

3941 

4002 

4 o 63 

4124 

4 i 85 

4245 

61 

7i5 

43o6 

4367 

4428 

4488 

4549 

4610 

4670 

473 i 

479 2 

4852 

61 

716 

4gi3 

4974 

5o34 

6096 

5156 

52i6 

0277 

5337 

5398 

6469 

61 

7*7 

3319 

558o 

0640 

3701 

5761 

5822 

588? 

5943 

6oo3 

6064 

61 

718 

6124 

6185 

6245 

63o6 

6366 

6427 

6487 

6548 

6608 

6668 

60 

7*9 

6729 

6789 

685o 

6910 

6970 

7 o 3 i 

7091 

.7162 

7212 

7272 

60 

720 

807332 

7393 

7453 

7 5 i 3 

7574 

7634 

7694 

7733 

7815 

7S75 

60 

721 

793.) 

7996 

8o56 

8116 

8176 

8236 

8297 

8357 

84*7 

8477 

60 

722 

8537 

8097 

8657 

8718 

8778 

8838 

8898 

8938 

9018 

9078 

60 

723 

9138 

9198 

9258 

9318 

9379 

94 3 9 

9499 

9 55 9 

9619 

9679 

60 

724 

0739 

9799 

9839 

99 l8 

9978 

®®38 

••98 

®i58 

®2l8 

*278 

60 

725 

86o338 0398 

0458 

o5i8 

0678 

o 63 7 

0697 

0757 

0817 

0877 

60 

726 

0937 

0996 

io56 

1 m6 

1176 

1236 

1290 

i355 

*4*^ 

*476 

60 

727 

1534 

1594 

i 654 

1714 

1773 

1833 

i 8 9 3 

1932 

2012 

2072 1 

60 

728 

2131 

2 191 

225l 

23lO 

2370 

2480 

2489 

2349 

2608 

2668 

60 

729 

2728 

2787 

2847 

2906 

2966 

3 o 23 

3o85 

3144 

3204 

3263 

60 

i 3 o 

863323 

3382 

3442 

35oi 

3561 

362 o 

368o 

3780 

3 799 

3858 

5 9 

7^1 

39*7 

3977 

4o36 

4096 

4133 

4214 

4274 

4333 

43 9 2 

4432 

09 

732 

431 1 

4070 

463 0 

4689 

4748 

4808 

4867 

4926 

4 9 85 

5 o 43 

3 9 

7 33 

3104 

5163 

3222 

6282 

5341 

5400 

5439 

5019 

5578 

5637 

39 

734 

5696 

5733 

5814 

5874 

5933 

5992 

60 51 

6110 

6169 

6228 

09 

7 43 

6207 

6346 

6406 

6463 

6324 

6583 

6642 

6701 

6760 

6819 

5 9 

736 

6S78 

6937 

6996 

7033 

7**4 

7173 

7232 

7291 

7350 

7409 

5 9 

737 

7467 

7626 

7585 

7644 

7703 

7762 

7821 

7880 

7939 

7998 

39 

733 

8o56 

8115 

8174 

8233 

8292 

83 5o 

8409 

8468 

8627 

8586 

39 

7 3 9 

8644 

8703 

8762 

8821 

8879 

8 9 38 

8997 

9036 

91 *4 

9*78 

3 9 

740 

869232 

9290 

9349 

94 o 3 

9466 

9325 

9384 

9642 

9701 

9760 

59 

741 

9818 

9877 

9980 

9994 

*•53 

® 1 I I 

®* 7° 

®220 

•287 

•345 

5 9 

742 

870404 

0462 

0321 

0379 

o638 

0696 

0736 

0813 

0872 

0930 

58 

743 

0089 

1047 

I 106 

1164 

1 223 

1281 

.339 

i 3 9 8 

1456 

1313 

58 

744 

1373 

1631 

1690 

1748 

r8o6 

1365 

i 9 23 

1981 

2040 

2098 

58 

740 

2136 

2215 

2273 

2331 

238 9 

2448 

25 o 6 

2 564 

2622 

268l 

58 

746 

2739 

2797 

2855 

2913 

2912 

3o3o 

3 o 88 

3 i 46 

3204 

3262 

58 

747 

3321 

3379 

3437 

3496 

3553 

3611 

3669 

2727 

3785 

3844 

58 

748 

3(302 

3960 

4018 

4076 

4*34 

4192 

425 o 

43 08 

4366 

4424 

58 

749 

4482 

454o 

4698 

4656 

4714 

4772 

4S3 o 

48S8 

49 ^ ' 

5oo3 

58 

i5o 

873061 

5i 19 

5 *77 

5235 

5298 

5351 

5409 

5466 

5524 

5582 

58 

75* 

0640 

6698 

5~i5b 

5813 

5871 

6929 

5987 

6o45 

6102 

6160 

58 

762 

6218 

6276 

6333 

6391 

6449 

6007 

6564 

6622 

6680 

6737 

58 

7 53 

6795 

6853 

6910 

6968 

7026 

7083 

7141 

7199 

7266 

73i4 

58 

754 

7871 

7429 

7487 

7544 

7602 

7669 

77*7 

7774 

7832 

7889 

58 

730 

7947 

8004 

8062 

8* 19 

8*77 

8234 

8292 

8349 

8407 

8464 

57 

766 

8522 

8379 

8037 

8694 

8732 

8809 

8866 

8924 

8981 

9039 

^7 

737 

9096 

gi53 

9211 

9268 

9 3 2 3 

g383 

9440 

9397 

9333 

96' 12 

^7 

738 

9669 

9726 

9784 

9841 

9898 

9936 

<* 9,3 

®»-70 

®I27 

®i85 

57 

7&9 

880242 

0299 

o 356 

o 4 i 3 

0471 

0328 

o585 

0642 

0699 

0766 

^7 

N. 

, 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

D . 















































































A TABLE OF LOGARITHMS FROM 1 TO 10,000. 13 


N. 

0 

1 


1 3 

I 3 

4 

5 

1 

i 6 

7 

8 

9 

D. 

760 

880814 

0871 

0928 

0985 

1042 

I0 99 

1156 

1213 

1271 

1328 

57 

761 

1385 

1442 

1499 

1556 

1613 

1670 

>727 

1784 

1841 

1898 

57 

762 

1955 

2012 

2069 

2126 

2i83 

2240 

2297 

2354 

2411 

2468 

5 7 

763 

2323 

258 i 

2638 

2696 

2762 

2809 

2866 

2923 

2980 

3o3~i 

57 

764 

8098 

3 i 5 o 

3207 

3264 

• 3321 

3377 

3434 

3491 

3548 

36o5 

37 

765 

3661 

3718 

3i-j5 

3832 

3888 

3940 

4002 

4059 

4115 

4172 

57 

766 

4229 

4285 

4342 

4399 

4455 

4312 

4669 

4625 

46S2 

4739 

5 7 

767 

4795 

4852 

4909 

4g65 

5o2 2 

5078 

5i35 

5192 

5248 

53 o 3 

37 

768 

5361 

5418 

5474 

5531 

5587 

5644 

5700 

5 7 5 7 

5813 

5870 

57 

769 

3926 

5 9 83 

6089 

6096 

6152 

6209 

6266 

6321 

6378 

6434 

56 

770 

886491 

6547 

6604 

6660 

6716 

6773 

6829 

6885 

6942 

6998 

56 

771 

7034 

711 X 

7167 

7223 

7280 

7 336 

7 3 9 2 

7449 

73 o 5 

7361 

56 

772 

7617 

7674 

7730 

7786 

7842 

7898 

7 9 53 

8011 

8067 

8123 

56 

773 

8179 

8236 

8292 

8348 

8404 

8460 

8516 

85j3 

8629 

8685 

56 

774 

8741 

8797 

8853 

8909 

8965 

9021 

9°77 

9i34 

9 >9° 

9246 

56 

775 

9802 

9 358 

94.14 

9470 

9026 

9682 

9688 

9694 

973° 

9806 

56 

776 

9862 

99 l8 

9974 

*°3o 

®*86 

®i4> 

*>97 

®'253 

®3 o 9 

®365 

56 

777 

890421 

0477 

o533 

o589 

0645 

0700 

0756 

0812 

0868 

0924 

56 

77« 

0980 

io35 

1091 

H47 

I 203 

1269 

1314 

1370 

1426 

1482 

56 

779 

i 537 

i5g3 

1649 

1705 

1760 

1816 

1872 

1928 

1983 

2039 

56 

780 

892095 

2i5o 

2206 

2262 

23 17 

2373 

2429 

2484 

2540 

25g5 

56 

781 

2651 

2707 

2762 

2818 

2873 

2929 

2986 

3 o 4 o 

3096 

3151 

56 

782 

3207 

3262 

3318 

33 7 3 

3429 

3484 

3540 

35g5 

3651 

3 706 

56 

7 83 

3762 

3817 

38 7 3 

3928 

3984 

4o3g 

4094 

4 i 5 o 

42 o 5 

4261 

33 

784 

4316 

4371 

4427 

4482 

4538 

4593 

4648 

4704 

4759 

4814 

55 

785 

78.6 

4870 

5423 

4926 

5478 

4980 

5533 

5o36 

5588 

5091 

5644 

5 i 4^> 

5699 

5201 

5754 

6267 

58o 9 

5312 
5864 

5367 

5920 

55 

55 

7«7 

5975 

6o3o 

6o85 

6140 

6195 

6231 

63o6 

636i 

6416 

6471 

55 

788 

6526 

6581 

6636 

6692 

6747 

6802 

6857 

6912 

6967 

7022 


789 

7°77 

7132 

7 i8 7 

7242 

7297 

7332 

7407 

7462 

7617 

7372 

5o 

790 

79 1 

897627 

8176 

7682 
8231 

rjz 

7792 

8341 

7847 

83 9 6 

79°2 

8451 

79 5 7 

85o6 

8012 
8561 

8067 
8615 

8122 

8670 

55 

55 

792 

8726 

8780 

8835 

8890 

8944 

8999 

9034 

9 :o 9 

9164 

9218 

55 

793 

9273 

9328 

g383 

9437 

9492 

9°47 

9602 

9666 

97>> 

9766 

55 
- ^ 1 

794 

9821 

9875 

99.30 

9985 

«<»39 

«®94 

®i49 

®2 o 3 

®258 

®3l2 

53 

793 

900367 

0422 

0476 

o53i 

0086 

0640 

0695 

0749 

0804 

0869 

33 

796 

0913 

0968 

1022 

1077 

1131 

1186 

1240 

1293 

1349 

1404 

33 

797 

U58 

1513 

1567 

1622 

1676 

1731 

1785 

1840 

l8 94 

1948 

34 

798 

2003 

2067 

2112 

2166 

2221 

2273 

2329 

2384 

2488 

2492 

34 

799 

2 547 

2601 

2655 

2710 

2764 

2818 

2873 

2927 

2981 

3o36 

54 

Boo 

QOjogo 

3144 

3199 

3253 

33o7 

336i 

3416 

3470 

3524 

3578 

54 

801 

3633 

368 7 

3741 

379D 

3849 

3 9 o 4 

8968 

4012 

4066 

4120 

34 

802 

4174 

4229 

4283 

4337 

4391 

4446 

4499 

4.553 

4607 

4661 

54 

So3 

4716 

4770 

4824 

4878 

4982 

4986 

5 o 4 o 

5094 

3148 

5202 

54 | 

804 

5256 

53io 

5364 

5418 

5472 

5526 

558o 

5634 

3686 

6742 

54 

8o5 

6796 

585o 

6904 

5958 

6012 

6066 

6119 

6173 

6227 

6281 

34 

806 

6335 

638o 

6443 

6497 

6551 

66o4 

6658 

6712 

6766 

6820 

54 

807 

68 7 i 

6927 

6981 

7o35 

7089 

7143 

7196 

7260 

7804 

7358 

53 

808 

809 

7411 
7949 

7465 

8002 

7619 

8 o 56 

75 7 3 

8110 

7626 

8163 

7680 

8217 

7734 

8270 

77 8 7 

8324 

7841 

83 7 8 

7893 

843i 

34 

54 

810 

908485 

8539 

8692 

8646 

8699 

8 7 53 

8807 

8860 

8914 

8967 

54 

811 

9021 

9074 

9128 

9181 

9235 

9289 

9342 

9396 

9449 

9008 

54 

812 

g556 

9610 

9663 

97 1 6 

9770 

9B28 

9 y 77 

99,80 

0464 

9984 

0037 

33 

813 

910091 

0144 

0197 

o 25 i 

o3o4 

o358 

0411 

o518 

o 5 ~i 

53 

814 

0624 

0678 

0731 

0784 

o838 

0891 

0944 

0998 

io5i 

1104 

53 

813 

11581 

1211 

1264 

1317 

137 

1424 

>477 

i 33 o 

1584 

1637 


816 

1690 

1743 

>797 

i85o 

igo3 

ig56 

2009 

2 o 63 

2116 

2169 

53 

817 

2222' 

2275 

2828 

2.381 

2435 

2488 

2341 

25 q 4 

2647 

2700 

33 

818 

2753 

2806 

2869 

2gi3 

2966 

3019 

3072 

3125 

8178 

3231 

53 

819 ; 

3284 

3337 

33go 

3443 

3496 

3549 

3 60 2 

3655 

3708 

3761 

jj 

N. j 

0 

1 

2 

3 j 

4 

5 

6 

7 

8 

9 

D. 














































































14 A TABLE OF LOGARITHMS FROM 1 TO 10,000. 


N. 

! ° | 

1 

j 2 

1 3 

4 

! 5 

6 

7 

8 

9 

D. j 

> 

820 

91 38 14 

3867 

3920 

| 3973 

4026 

4079 

4 i 32 

4184 

4237 

4290 

53 

S21 

4343 

4396 

1 4449 

4602 

4555 

4608 

4660 

47 1 G 

4766 

4819 

53 

822 

4872 

4925 

i 4977 

5 o 3 o 

5 o 83 

5 1 36 

6189 

5241 

5294 

5347 

53 

823 

5400! 

5453 

55 o 5 

5558 

56 11 

1 5664 

5 7 i 6 

6769 

5822 

5875 

53 

824 

5927 

5980 

1 6 o 33 

6 oS 5 

61 38 

619 1 

6243 

6296 

6349 

6401 

53 

823 

6454 

6507 

; 6569 

6612 

6664 

: 6717 

6770 

6822 

68 7 5 

6927 

531 

826 

6980 

7 o 33 

1 7 o 85 

71 38 

7190 

! 7243 

7295 

7348 

74 oo 

7403 

53 ! 

827 

7606 

7668 

7611 

7663 

7716 

j 7768 

7820 

7873 

7920 

797 S 

52 

1 828 

8 o 3 o 

8 o 83 

' 81 35 

8188 

8240 

8293 

8345 

83 97 

8460 

8002 

52 

j 829 

8555 

8607 

, 865 g 

8712 

1 8764 

i 8816 

8869 

8921 

8 97 3 

9026 

52 1 

83 o 

1919078 

gi 3 o 

gi 83 

9 235 

9287 

; 9H0 

9392 

9444 

9496 

9649 

52 J 

83 1 

j 9601 

9653 

9706 

9738 

9810 

9862 

99 1 4 

9967 

«®ig 

••71 

52 ! 

832 

'920123 

0176 

1 0228 

0280 

o 332 

o 384 

0436 

0480 

o 54 i 

0693 

52 j 

833 

0645 

0697 

0749 

0801 

o 853 

0906 

og 58 

1016 

1062 

: 114 

52! 

834 

1166 

1218 

1270 

13 2 2 

1 3 7 4 

1426 

1478 

i 53 o 

1 582 

1634 

52 1 

835 

1686 

1 7 38 

1790 

1842 

1894 

1946 

1998 

2 o 5 o 

2102 

2 i 54 

52 

836 

2206 

2258 

23 l 0 

2362 

2314 

2466 

25 18 

25 7 o 

2622 

2674 

52 [ 

83 7 

2725 

2777 

2829 

2S8I 

29 53 

2985 

3 o 3 7 

3089 

3 140 

3192 

02| 

838 

3244 

3296 

3.548 

3399 

345 £ 

3 oo 3 

3555 

3607 

3658 

3 7 io 

52 

889 

37O2; 

38 U 

3865 

3917 

3969 

4021 

4072 

4124 

4176 

4228 

52; 

840 

9^279 

433 i 

4383 

4434 

4486 

4538 

458 q 

4641 

4693 

4744 

52 

841 

4796 1 

4848 

4899 

4901 

5 oo 3 

5 o 54 

5 106 

0107 

0209 

526 i 

02! 

842 

551 2; 

5364 

54 1 5 

5467 

55 18 

55 7 o 

5621 

56 7 3 

5 7 2 D 

5776 

52 j 

843 

6828! 

5879 

5 g 3 1 

5982 

6 o 34 

6 o 85 

61 3 7 

6188 

6240 

6291 

5 i 

844 

6342 j 

63 g 4 

6445 

6497 

6648 

6600 

665 1 

6702 

6754 

68 o 5 

5 i 

845 

68671 

6908 

6 g 5 g 

7011 

7062 

7114 

7165 

7216 

7268 

7 3| 9 

5 ! 

846 

787° 

7422 

7473 

7624 

7076 

7627 

7678 

7730 

7781 

7832 

51 

847 

7 < 8 o 3 

7935 

7986 

8 o 3 7 

8088 

8140 

9191 

8242 

8293 

8345 

5 i 

848 

8396 1 

8447 

8498 

8549 

8601 

8652 

8 7 o 3 

8 7 54 

S 8 o 5 

8867 

5 i 

849 

8908] 8969 

9010 

9061 

9112 

9 i 63 

9215 

9266 

9 3 i 7 

9368 

5 i 

85 o 

929419 

9470 

g 52 i 

9^2 

9623 

9674 

9725 

9776 

9827 

9879 

5 i 

85 1 

998° 

9981 

«®32 

*•83 

® 1 34 

®i 85 

*236 

*287 

*338 

° 38 9 

5 i 

852 

930440 | 

0491 

0542 

0692 

0643 

0694 

0745 

0796 

0847 

0898 

5 i 

853 

0949 1 

1000 

io 5 i 

1 102 

11 53 

1204 

1254 

1 3 o 5 

1 356 

1407 

5 i 

854 

i 458 j 

1609 

i 56 o 

1610 

1661 

1712 

i 7 63 

1814 

i860 

1915 

5 1 

855 

1966 

2017 

2068 

2118 

2169 

2220 

2271 

2322 

23 7 2 

2423 

5 i 

856 

2474 

2624 

20 7 0 

2626 

2677 

2727 

2778 

2829 

2879 

2g3o 

5 i 

867 

29811 

3 o 3 i 

3o82 

3133 

3 1 83 

3234 

3285 

333 o 

3386 

3437 

5 i 

858 

3487 1 

3538 

3689 

3639 

3690 

3 7 4 o 

3791 

3841 

3892 

3 9 43 

5 i 

859 

3 99 3 1 

4044 

4094 

4 i 43 

4 ig 5 

4246 

4296 

4347 

4397 

4448 

5 i 

860 

98449BI 

4549 

4599 

465 o 

4700 

4 7 5 i 

4801 

4852 

4902 

4 g 53 

5 o 

861 

5 oo 31 

5 o 54 

5 104 

5 i 54 

52 o 5 

5255 

53 o 6 

5356 

5406 

5407 

5 o 

862 

5007! 

5558 

56 o 8 

5658 

5709 

5 7 5 g 

5809 

586 o 

5 gio 

5960 

5 o 

863 

60111 

6061 

6111 

6162 

6212 

6262 

63 1 3 

6363 

6413 

6463 

00 

864 

65 14 

6564 

6614 

6665 

671 5 

6766 

' 681 5 

6865 

6916 

6966 

5 o 

865 

7016 

7066 

l 11 ! 

7167 

7217 

7267 

7317 

7867 

74 i 8 

7468 

5 o 

866 

7518 

7 568 

7618 

7668 

7718 

7769 

7819 

0869 

79 1 9 

7969 

5 o 

867 

8oig| 

8069 

8119 ' 

8169 1 

8219 

8269 

8320 

83 7 o 

8420 

8470 

5 o 

868 

8520 

85 7 o 

8620 

8670 

8720 

8770 

8820 

O870 

8920 

8970 

5 o 

869 

9020, 

9070 

9120 

9 1 7 ° 

9220 

9270 

q 320 

/ 

9369 

9419 

9469 

5 o 

870 

939619 

9669 

9619 

9669 

9719 

9769 

9819 

9869 

99 1 8 

9968 

5 o 

871 

940018 

0068 

0118 

0168 

0218 

0267 

o 3 i 7 

o 36 7 

0417 

0467 

5 o 

872 

0616 

o 566 

0616 

0666 

0716 

0766 

081 5 

o 865 

091 5 

0964 

5 o 

8 7 3 

i 014 

1064 

1114 

11 63 

121 3 

1263 

13 1 3 

1 362 

1412 

1462 

5 o 

874 

i 5 i 1 

i 56 i 

1611 

1660 

1710 

1760 

1809 

1 85 g 

1909 

1968 

5 o 

876 

20oS j 

2 o 58 

2107 

21 5 7 

2207 

2256 

23 o 6 

2355 

24 o 5 

2455 

00 

876 

2004 

2004 

26o3 

2653 

2702 

2762 

2801 

285 1 

&901 

2960 

5 o 

&77 

3 ooo 

3049 

3 ogg 

3 i 4 S 

3198 

3247 

3297 

3346 

33 o 6 

3440 

09 

878 

0495 

3544 

35 g 3 

3643 

3692 

3742 

379 1 

3841 

38 go 

3 g 3 g 

5 g 

879 

0989 

4 o 38 

4088 

41 3 7 

4i86 

4236 

4285 

4335 

4384 

4433 

5 g 

u. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

I). 

















































































A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 15 


N. 

0 

I 

2 

3 

4 

i 5 

6 

7 

8 

9 

D. 

8So 

9 4448v. 

4532 

458l 

4631 

4680 

4729 

4779 

4828 

4877 

4927 

4q 

881 

882 

497^ 

546c 

3023 

5518 

5074 

5567 

8124 

56i6 

5173 

5665 

5222 

6716 

5272 

6764 

532i 

58i3 

5370 

5862 

9419 

5qi2 

49 

4o 

883 

6961 

601 c 

| 6039 

6108 

6157 

6207 

6256 

63o5 

6354 

6403 

4q 

884 

6435 

65oi 

6551 

6600 

6649 

6698 

6747 

6796 

6845 

6894 

4o 

885 

6940 

6992 

7041 

7090 

7*4o 

7189 

7238 

1 7287 

7336 

7385 

4o 

886 

7434 

7483 

7532 

758 i 

763o 

7679 

7728 

I 7777 

7826 

7875 

4q 

887 

7924 

7973 

8022 

8070 

8119 

8168 

8217 

8266 

8315 

8364 

4q 

888 

8418 

8462 

8511 

856o 

8609 

8657 

8706 

8755 

8804 

8853 

4q 

889 

8902 

8931 

8999 

9°48 

j 9°97 

9146 

9 X 9 5 

9244 

9292 

9341 

49 

890 

949390 

9439 

9488 

9380 

9 585 

9634 

9 683 

973i 

9780 

9829 

49 

891 

_ 9 8 7 8 

9926 

9973 

OC 24 


*121 

®i70 

*219 

•267 

•3i6 

49 

892 

9 5 o 365 

0414 

0462 

! o5i 1 

o56o 

0608 

0657 

0706 

0764 

o8o3 

49 

893 

o 85 i 

0900 

0949 

°997 

1046 

1095 

ii 43 

1192 

1240 

1289 

49 

894 

1338 

i386 

1435 

1483 

153 2 

i58o 

1629 

1677 

1726 

1775 

49 

896 

1828 

1872 

1 IQ20 

x 9 6 9 

2017 

2066 

2114 

2163 

2211 

2260 

43 

896 

23 o 8 

2356 

2 40 5 

2453 

2502 

26D0 

25 9 9 

2647 

2696 

2744 

48 

897 

2792 

2841 

2889 

2938 

2986 

3o34 

3o83 

3131 

3180 

3228 

48 

898 

3276 

3325 

3373 

342 i 

3470 

3518 

3566 

3615 

3663 

3711 

48 

899 

3760 

38o8 

3856 

3905 

3953 

4001 

4049 

4098 

4i46 

4194 

48 

900 

9 54243 

4291 

433 9 

4387 

4435 

4484 

4532 

458o 

4628 

4677 

48 

901 

4723 

4773 

4821 

4869 

49l8 

4966 

5 oi 4 

5 o 62 

5i 10 

5158 

48 

902 

D207 

3255 

53o3 

5351 

5399 

5447 

54 9 5 

5543 

55 9 2 

5640 

48 

903 

5688 

5736 

5784 

5832 

588o 

5 9 28 

5976 

6024 

6072 

6120 

48 

904 

6168 

6216 

6268 

6313 

636i 

6409 

6457 

65o5 

6553 

6601 

43 

906 

6649 

6697 

6745 

6793 

6840 

6888 

6 9 36 

6984 

7032 

7080 

48 

906 

7128 

7 1 76 

7224 

7272 

7320 

7 368 

7416 

7464 

7512 

7359 

48 

9°7 

7607 

7655 

77 o 3 

776i 

7799 

7847 

7894 

7942 

7990 

8o38 

48 

908 

8086 

8134 

8181 

8229 

8277 

8325 

83 7 3 

8421 

8468 

8516 

48 

9°9 

8564 

8612 

8689 

8707 

8755 

88o3 

885o 

8898 

8946 

8994 

48 

910 

9 5 9 o 4 i 

9089 

9137 

9185 

9232 

9280 

9328 

9375 

9423 

947 1 

48 

9 11 

9 5 i 8 

9866 

9614 

9661 

9709 

9757 

9804 

9802 

9900 

9947 

48 

912 

9993 

©»42 

O»Q0 

®i38 

«185 

•233 

•280 

•328 

•376 

•423 

48 

9 i 3 

960471 

o5i8 

o566 

0613 

0661 

0709 

0756 

0804 

oS5i 

0899 

48 

914 

0946 

0994 

1041 

1089 

1136 

1184 

I 23 I 

1279 

i 326 

1374 

47 

9 t 5 

1421 

1469 

1516 

1563 

r 611 

1658 

1706 

1703 

1801 

1848 

47 

916 

1896 

1943 

1990 

2o38 

2o85 

2132 

2180 

2227 

2275 

232-2 

47 

9*7 

236 9 

2417 

2464 

251 I 

2559 

2606 

2653 

2701 

2748 

2 79 5 

47 

918 

2843 

2890 

2937 

2985 

3o32 

3079 

3i26 

8174 

3221 

3268 

47 

919 

3316 

3363 | 

34io 

3437 

35 o 4 

3552 

35 99 

3646 

36 9 3 

3741 

47 

920 

963788 

3835 

3882 

3929 

3 977 

4024 

4071 

4i 18 

4165 

4212 

47 

921 

4260 

4307 

4334 

4401 

4448 

44 9 3 

4542 

45 9 o 

4637 

4684 

47 

922 

4731 

4773 

4825 

4872 

4919 

4966 

5oi3 

5o6i 

5108 

5i 55 

47 

923 

5202 

5249 

3296 

5343 

53go 

5437 

5484 

5531 

0578 

5625 

47 

924 

5672 

5719 

5766 

58i3 

586o 

5 9 o7 

5 9 54 

6001 

6048 

6096 

47 

9 23 

6l42 

6189 

6236 

6283 

6329 

63 7 6 

6423 

6470 

65i 7 

6564 

47 

9 26 

66l I 

6658 

6705 

6782 

6799 

684 3 

6892 

6 9 3 9 

6986 

7o33 

47 

92 7 

7080 

7127 

7173 

7220 

7267 

7314 

736 i 

7408 

7454 

j 5 oi 

47 

928 

7548 

7893 

7642 

7688 

7735 

7782 

7829 

7875 

7922 

7969 

47 

929 

8016 

8062 

8109 

8156 

82o3 

8249 

8296 

8343 

83 9 o 

8436 

47 

930 

768483 

853o 

8676 

8623 

8670 

8716 

8 7 63 

88 ro 

8856 

8 9 o3 

47 

9 3 I 

8950 

8996 

9043 

9090 

9136 

9183 

9229 

9276 

9 323 

9 36 9 

47 

9 32 

9416 

9463 

9609 

9556 

9602 

9649 

9 6 9 5 

9742 

9789 

9835 

47 

9 33 

9882 

9928 

9973 

«®2I 

°®68 

®i 14 

w i6i 

•207 

®254 

®3oo 

47 

9^4 

>70347 

o3g3 

0440 

0486 

o533 

o5 79 

0626 

0672 

0719 

0765 

40 

q35 

0812 

o853 | 

0904 

0961 

0997 

1044 

1090 

1137 

1183 

1229 

46 

9 36 

1276 

1322 

1369 

1415 

1461 

i5o8 

1554 

1601 

1647 

1693 

46 

9 3 7 

1740 

1786 

i832 

1879 

1920 

1 97 1 

2018 

2064 1 

2110 

2157 

46 

9 38 

2203 

2249 

2295 

2342 

2388 

2434 

2481 

2527 j 

2673 

2619 

46 

9 3 9 

2666 

2712 

2788 

2804 

2851 

2897 

2943 

2989 j 

3o35 

3082 

46 

N 

0 

I ’ 

2 

3 4 

4 

5 

6 

7 

8 

9 

i). 


25 



















































































































i6 A TABLE OF LOGARITHMS FROM 1 TO 10 , 000 . 


N. 

0 

. 

2 

3 

4 

5 

6 

1 7 

8 

j 9 

1 

940 

973128 

8174 

3220 

3266 

3313 

335g 

34 o 5 

3451 

3497 

3543 

46 

941 

3590 

3636 

3682 

3728 

3774 

3820 

3866 

8913 

8969 

I 400 5 

I 46 

942 

4o5i 

4097 

4 i 43 

4189 

4235 

4281 

4327 

4374 

4420 

4466 

46 

943 

45i2 

4538 

4604 

465 o 

4696 

4742 

4-88 

4834 

1880 

1 4926 

46 

944 

4972 

5oi8 

5o64 

5 i 10 

5156 

5202 

1 5248 

j 5294 

j 534o 

5386 

46 

945 

5432 

5478 

5524 

5570 

56i6 

5662 

1 5707 

5 7 53 

I 5799 

5845 

, 46 

946 

5891 

5 9 3 7 

5 9 83 

6029 

6075 

6121 

1 6167 

I 6212 

6268 

63 ci . 

46 

947 

6330 

63o6 

6442 

6488 

6533 

6579 

6625 

6671 

6717 

1 6768 

46 

948 

680S 

6854 

6900 

6946 

6992 

7037 

7083 

7129 

7175 

| 7220 

46 

949 

7266 

7 3l2 

7338 

74 o 3 

7449 

7495 

7541 

7686 

7632 

7678 

46 

<55o 

95 i 

97 3Ilfi Itl 

7815 
8272 

7861 
8317 

7906 

8363 

7 9 52 

8409 

7998 

8454 

8043 

85oo 

8089 

8546 

8135 
8691 

46 

46 

02 

8637 

8683 

8728 

3774 

8819 

i8865 

8911 

8 9 56 

9002 

9047 

46 

953 

9093 

9i38 

9184 

9230 

9275 

9 32i 

9366 

9412 

9457 

9608 

46 

954 

9548 

9094 

9639 

9 685 

9730 

9776 

9821 

9867 

9912 

9908 

46 

955 

980003 

0049 

0094 

0140 

oi85 

023 x 

0276 

0322 

o36 7 

0412 

45 

956 

0468 

o5o3 

0349 

0594 

0640 

o685 

0730 

0776 

0821 

0867 

45 

907 

0912 

0967 

ioo3 

1048 

io 9 3 

1139 

1184 

1229 

1276 

1320 

45 

958 

i366 

1411 

1456 

i 5 oi 

1547 

1592 

1637 

1683 

1728 

1773 

45 

969 

1819 

1864 

1909 

1954 

2000 

2046 

2090 

2i35 

2181 

2226 

45 

960 

982271 

23 i 6 

2362 

2407 

2452 

2497 

2543 

2588 

2633 

2678 

45 

961 

2723 

2769 

2814 

2859 

2904 

2949 

2994 

3 040 

3o85 

3i3o 

45 

962 

3i75 

3220 

3265 

33io 

3356 

3401 

3446 

3491 

3536 

358i 

45 

963 

3626 

3671 

3716 

3762 

3807 

3852 

3897 

3 o 42 

3987 

4 o 32 

45 

964 

4077 

4122 

4167 

4212 

4257 

43 o 2 

4347 

4392 

4437 

4482 

45 

965 

4527 

4372 

4617 

4662 

4707 

4 7 52 

4797 

4842 

4887 

4932 

45 

966 

4977 

5022 

5067 

5112 

5157 

5202 

5247 

5292 

5337 

5382 

45 

967 

5426 

5471 

55i6 

556i 

56o6 

5651 

5696 

5741 

6786 

583o 

45 

968 

58 7 5 

5920 

5 9 65 

6010 

6o55 

6100 

6144 

6189 

6234 

6279 

45 

969 

6324 

6369 

64 i 3 

6458 

65o3 

6548 

65 9 3 

6637 

6682 

6727 

45 

970 

986772 

6817 

6861 

6906 

6951 

6996 

7040 

7080 

7i3o 

7175 

45 

97i 

7219 

7264 

7 3°9 

7 353 

7398 

7443 

7488 

7532 

7577 

7^22 

45 

972 

7666 

77 11 

77 56 

7800 

7845 

7890 

7934 

7979 

8024 

8068 

45 

97 3 

8113 

8137 

8202 

8247 

8291 

8336 

838i 

8423 

8470 

85i4 

45 

974 

8669 

8604 

8648 

8693 

8737 

8782 

8826 

8871 

8916 

8960 

45 

973 

9000 

9049 

9094 

91J8 

91 S3 

9227 

9272 

93i6 

9361 

9400 

45 

976 

9430 

9494 

9539 

9 583 

9628 

9672 

97*7 

9761 

9806 

9860 

44 

977 

9895 

9939 

9983 

*®28 

®® 7 2 

®i 17 

®i6i 

®2o6 

®25 o 

•294 

44 

978 

99 o 33 q 

o383 

0428 

0472 

o5i6 

o56i 

o6o5 

o 65 o 

0694 

0738 

44 

979 

o 7 83 

0827 

0871 

0916 

0960 

1004 

1049 

1093 

1137 

1182' 

44 

980 

991226 

1270 

1315 

i 35 9 

i4o3 

1448 

1492 

1536 

i58o 

1626 

44 

981 

1669 

1713 

1758 

18o-> 

1846 

1890 

1935 

! 979 

2023 

2067 

44 

982 

2111 

2156 

2200 

22, i 1 

2288 

2333 

2377 

2421 

2465 

2509 

44 

983 

2554 

25o8 

2642 

2 686 

2730 

2 774 

2819 

2863 

2907 

2951 

44 

984 

2995 

3 oJ 9 

3o83 

3127 

3 i 7 2 

32 16 

3260 

33 o 4 

3348 

3392 

44 

9 85 

3436 

3480 

3524 

3568 

36i3 

365 7 

3 7 oi 

3745 

3789 

3833 

44 

986 

38 77 

3921 

3965 

4009 

4 o 53 

4097 

4141 

4 i 85 

4229 

4273 

44 

987 

43i7 

4361 

44o 5 

4449 ! 

449 3 

4537 

458 i 

4625 

4669 

4 7 i 3 

44 

988 

4737 

4801 

4843 

4889 

4933 

4977 

5021 

5o65 

5108 

5152 

44 

989 

5196 

5240 

5284 

5320 

53 7 2 

5416 

5460 

55 o 4 

5547 

5591 

44 

990 

995635 

J679 

5723 

5767 

58i 1 

5854 

5898 

5942 

5986 

6o3o 

44 

991 

6074 

6117 

6161 

6206 

6249 

6293 

633 7 

638o 

6424 

6468 

44 

' 99 2 

6512 

6555 

6599 

6643 

6687 

6731 

5774 

6818 

6862 

6906 

44 

99 3 

6949 

6993 

7037 

7080 

7124 

7168 

7212 

7255 

7299 

7343 

44 

994 

7386 

7430 

7474 

7617 

7 56 i 

7 6o5 

7648 

7692 

7786 

7779 

44 

993 

7823 

7867 

7910 

7954 

7998 

8434 

8041 

8o85 

8129 

8172 

8216 

44 

996 

8239 

83o3 

8347 

8.390 

8477 

8521 

8564 

8608 

8652 

44 

997 

86 9 5 

8739 

8782 

8826 

8869 

8913 

8966 

9000 

9043 

9087 

44 

998 

9131 

9H4 

9218 

9261 

93 o 5 

9848 

9 3 9 2 

9435 

9479 

9522 

44 

999 

9563 9609 

9652 

9696 

9739 

97 83 

9826 

9870 

99 l3 

9967 

43 

N. 

0 

1 

2 

3 

4 

5 

* 6 

7 

8 

9 

1 ). 





























































































A TABLE 


OF 


LOGARITHMIC 

SINES AND TANGENTS 

FOR EVERY 

DEGREE AND MINUTE 

OF THE QUADRANT. 


Remark. ?The minutes in the left-hand column of eacra 
page, increasing downwards, belong to the degrees at the 
top; and those increasing upwards, in the right-hand column, 
belong to the degrees below. 



L8 (0 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. ' Cosine 

D. 

Tang. 

IX 

Cotang. 


0 

1 

2 

3 

4 

t 

I 

9 

10 

II 

12 

13 

14 

\l 

'*9 

20 

21 

22 

23 

24 

25 

26 
27 
0 8 

g 

31 

32 

33 

34 

35 

36 

37 

38 

?q 

40 

41 

42 

43 

44 

45 

46 

47 

48 

fo 

51 

52 

53 

54 

55 

56 

59 

1 60 

6*463726 

764766 

940847 

7•066786 

162696 
241877 
308824 
366316 
417968 

463725 

7-5ooi18 
542906 
677668 

609853 

639816 

667845 

694173 

718997 

742477 

764764 

7-780943 
606i46 

825461 
843934 
861662 
878695 
8 9 5 o 85 
910879 
926119 
940842 

7- 9 55 o 82 
968870 

982233 

8.8?# 

020021 

031019 

043601 

064781 

065776 

8- 076500 
o36 9 65 
097183 
107167 

116926 
126471 

135810 

144953 

163907 
162681 

8-171280 
179713 
187985 
196102 
2040->0 

2:: Sq 5 
219681 
227134 
234557 
241866 

5ot7- 17 

2934-86 

2082-3I 

1615• 17 

1319• 68 
iii 5-75 

066•53 
802-54 
762-63 

689-88 

629-81 

679-36 

536-41 

499-38 

467-14 
438-8i 
4i3-72 
391-35 
371-27 
353•15 

336-72 
321*75 
3o8-oj 

295-47 
283-88 
273-17 
263•20 

253-99 

2 45•38 
237-33 

229-80 

222-73 

216-08 

209-81 

20.8-90 

198-31 

193-02 

188-01 

183•25 
178-72 

I74-4I 

170*31 

166*39 

162*66 

109-08 

155-66 
162*38 
149-24 
146-22 
143-33 

i4o-54 

137•86 

135•7 9 

132•80 

! 3o■41 
128-10 

I 126-87 
123-72 

121-64 

119-63 

10-000000 

000000 

000000 

000000 

000000 

000000 

9-999999 

999999 

999999 

999999 

999998 

9-999998 

999997 

999997 

999996 

999996 

999990 

999995 

999994 

99999J 

999993 

9-999992 

999991 

999900 

999989 

999988 

999988 

999987 

999986 

999985 

-999983 

9-999982 

99^981 

999980 

999979 

999977 

999976 

999975 

999973 

999972 

999971 

9.999969 

999968 

999966 

999964 

999963 

999961 

999959 

999968 

99995j 
9 999 54 

9-999952 
999960 
999948 
999946 

999944 

999942 

999940 

999938 

999936 

999934 

• 00 

• 00 

• 00 

• 00 

• 00 

• 01 

•01 

•01 

•01 

•01 

• 01 

-01 

• 01 

■ 01 

• 01 

• 01 

*01 

• 01 

•01 

• 01 

•01 

•01 

•01 

•02 

•02 

•02 

■ 02 

•02 

•02 

•02 

•02 

•02 

•02 

•02 

•02 

•02 

•02 

•02 

•02 

•02 

• 02 

• 02 

• 02 
•o3 
•o3 
•o3 
•o3 
•o3 
•o3 
•o3 

•o3 

•o3 

•o3 

• o3 
•o3 
•04 

• 04 

• 04 

I -04 

1 -04 

0-000000 

6- 463726 
764756 
940847 

7- 066786 
162696 
241878 
3o8825 

366817 

41797° 

463727 

7-5o5i2o 

642909 

677672 

609857 

63 9 82o 

667849 

694179 

719004 
742484 
764761 

7-786961 
806155 
826460 
843944 
S61674 
878708 
89.6099 

910804 

926184 

9 4o858 

7- 9 55ioo 

968889 

982263 

996219 

8- 007809 
020040 
081946 
043627 
054809 
066806 

8-076531 

086997 

097217 

107202 

116963 

126610 

135851 
144096 
158902 
162727 

8-171328 
170763 
i88o36 
196166 
204126 

211963 
219641 
227196 
234621 
241921 

5017-17 
2934-83 
2082-3 1 
i 6 i 5-17 
1319-69 
1110-78 

996-53 
802-54 
762-63 
689-88 

629-81 

579-33 

536-42 

499•39 
467 • 10 

438-82 

413 * 73 
391-36 
371-28 
35i-35 

336-73 
321-76 
3o8-o6 
295-49 
283-90 
273-18 

263- 25 

264- 01 
246-40 
237*35 

229-81 
222*76 
216-10 
200-83 
200-92 
198-33 
193-06 

188 • o3 

183 • 2 7 

178-74 

174-44 

170-34 

166-42 

162-68 

159-10 

155-68 

I 52 - 4 1 
149-27 
146-27 
143-36 

140-07 

137-90 

135 - 32 

1 32 -84 
i 3 o -44 
i 128-14 
125-90 
123-76 
121-68 

1 19-67 

Infinite. 
13-536274 
235244 j 
069163 ! 
12-934214 ! 
8373o4 
768122 
691175 
633183 
582 o 3 o 
536273 

12-494880 
457091 
422328 i 
390143 1 
36oi8o j 
33 215 1 : 
3o582i | 
280997 1 
207016 j 
235239 

12*214049 i 
193840 j 
174540. : 
156o56 
138326 - 
121292 
104901 
089106 
073866 
069142 

12 • 044900 
o3i 111 
017747 
004781 

11*992191 
979905 
968060 

956473 
* 940191. 

934194 

11-923469 
9i3oo3 
002783 
802797 
883007 
873490 

864149 

855oo4 

846048 

837273 

11-828672 
820267 

811964 
8o3844 
796874 
788047 
780.309 
77280O 
765.879 
758079 

60 

5? 

57 

56 

55 

54 

53 

52 

01 

So 

40 

48 

47 

46 

45 

44 

43 

42 

41 

4o 

3$ 

37 

36 

35 

34 

33 

32 

3i 

3o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

IQ 

18 

17 

16 

i5 

14 

i3 

12 

11 

l 10 

9 

8 

1 7 

6 

5 

4 

3 

2 

1 

! 0 


Cosine 

D. 

Sine J 

! Cotang. 

D. 

! Tang. 

M. 


(89 DEGREES.) 








































































SINES AND TANGENTS. (1 DEGREE.) 


19 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

8 - 24 i 855 

119-63 

9-999934 

• 04 

8-241921 

119-67 

11 -758079 

60 

i 

249033 

117-68 

999932 

• 04 

249102 

117.72 

750898 

5 9 

2 

256094 

11 5 •80 

999929 

•04 

256 2 65 

11 5 •84 

743835 

I sA 

3 

263042 

113-98 

999927 

-04 

263 11 5 

114-02 

736885 

1 57 

4 

269881 

112 • 21 

999925 

• 04 

269956 

112-25 

730044 

56 

5 

276614 

no- 5 o 

999922 

• 04 

276691 

iio -54 

723309 

i 55 

6 

283243 

io 8-83 

999920 

•04 

283323 

108-87 

716677 

! 5 3 

7 

2S9773 

107-21 

999918 

•04 

289806 

107-26 

710144 

53 

8 

296207 

io 5-65 

9999 1 6 

• 04 

296292 

106-70 

708708 

I 52 

9 

302546 

104•1 3 

999913 

•04 

302634 

io4-18 

697366 

5 i 

10 

308794 

102-66 

999910 

-04 

3 o 8884 

102-70 

691116 

1 5 o 

ii 

8-314904 

IOI-22 

9.999907 

•04 

8• 3 16046 

101-26 

11-684954 

i 49 

12 

321027 

. 99-82 

999905 

•04 

321122 

99-87 

678078 

1 48 

i 3 

327016 

98-47 

999902 

• 04 

327114 

98 • 5 1 

672886 

! 47 

14 

332924 

97*14 

999899 

• o 5 

333025 

97.19 

666975 

46 

ID 

338753 

90-86 

999897 

• o 5 

338856 

96-90 

661144 

45 

16 

3445 o 4 

94-60 

999894 

• o 5 

344610 

94-65 

655390 

44 

*7 

18 

35 oi 8 i 

355783 

9 3-38 
92-19 

999891 

999888 

• o 5 

• o 5 

350289 

355890 

93-43 

92-24 

649711 

644 io 5 

43 

42 

*9 

36 i 3 i 5 

91 -o 3 

999886 

• o 5 

36 i 43 o 

01-08 

638570 

41 

20 

366777 

89.90 

999882 

• o 5 

366895 

89.95 

633 1o 5 

40 

21 

8-372171 

88-80 

9-999879 

•o 5 

8-372292 

88-85 

11-627708 

39 

22 

377499 

87-72 

999876 

• o 5 

377622 

87-77 

622378 

38 

23 

382762 

86-67 

999873 

• o 5 

382889 

86-72 

617111 

37 

24 

387962 

85-64 

999870 

• o 5 

388092 

85-70 

611908 

36 

25 

393101 

84-64 

999867 

• o 5 

393234 

84-70 

606766 

35 

26 

398179 

83-66 

999864 

• o 5 

398316 

83 - 7 i 

6 oi 685 

34 

27 

403199 

82-71 

999861 

• o 5 

4 o 333 S 

82-76 

596662 

33 

28 

408161 

8 i *77 

999808 

•o 5 

4 o 83 o 4 

81-82 

591696 

32 

29 

4 i 3 o 68 

80 -86 

999864 

• o 5 

4 i 32 i 3 

80-91 

586787 

3 i 

3 o 

417919 

79.96 

999851 

• 06 

418068 

80-02 

581932 

3 o 

3 i 

8-422717 

79-09 

9-999848 

• 06 

8-422869 

79-14 

11•5771 3 1 

29 

32 

427462 

78-23 

999844 

-06 

427618 

78 - 3 o 

372382 

28 

33 

432 1 56 

77.40 

999841 

• 06 

4323 i 5 

77-45 

56 7 685 

27 

34 

4368 oo 

76-67 

999838 

-06 

436962 

76-63 

563 o 38 

26 

35 

441394 

75.77 

999834 

• 06 

44i 36 0 

7 5-83 

558440 

25 

36 

445941 

74-99 

999831 

• 06 

446110 

75 -o 5 

553890 

24 

37 

45 o 44 o 

74-22 

999827 

• 06 

45 o 6 i 3 

74-28 

549387 

23 

38 

454893 

73-46 

999823 

• 06 

455070 

73-52 

54493 o 

22 

3 9 

439801 

72-73 

999820 

• 06 

459481 

463849 

72-79 

540319 

21 

4 o 

463665 

72-00 

999816 

• 06 

72-06 

536 i 5 i 

20 

4 i 

8-467985 

71-29 

q-qqq8i2 

• 06 

8-468172 

71-35 

11- 53 iS 28 

IQ 

42 

472263 

70-60 

999809 

• 06 

472454 

70-66 

527346 

l8 

43 

476498 

69.91 

999803 

-06 

476693 

69-98 

523307 

17 

44 

480693 

69-24 

999801 

• 06 

480892 

69. 3 i 

519108 

l6 

45 

484848 

68 - 5 9 

999797 

-07 

485 o 3 o 

68 • 65 

5 14950 

i 5 

46 

488963 

67-94 

999793 

-07 

489170 

68-oi 

5 io 83 o 

14 

47 

493040 

67-31 

999700 

999786 

.07 

493260 

67-88 

506700 

i 3 

48 

497078 

66-69 

-07 

497293 

66-76 

502707 

12 

49 

5 oioSo 

66-o8 

999782 

• 07 

501298 

66 -1 5 

498702 

11 

5 o 

5 o 5 o 45 

65-48 

999778 

.07 

605267 

65-55 

494733 

10 

5 i 

8-508974 
512867 

64-89 

9-999774 

.07 

8-509200 

64-96 

11•490800 

0 

52 

64 - 3 1 

999769 

-07 

613098 

64 • 09 

486902 

8 

53 

516726 

63-75 

999760 

.07 

516961 

63-82 

483 o 39 

7 

54 

52 o 55 i 

63-19 

999761 

-07 

520790 

63 • 26 

479210 

6 

55 

524343 

62-64 

999757 

-07 

524586 

62-72 

476414 

5 

56 

628102 

62-11 

999753 

-07 

628349 

62-18 

47i 65 i 

4 

57 

53 i 828 

6 i -58 

999748 

■ 07 

532 o 8 o 

61 -65 

467920 

3 

58 

535523 

61 -06 

999744 

.07 

535779 

61 • 1 3 

464221 

2 

5 9 

539186 

60 -55 

999740 

-07 

539447 

540084 

60-62 

46 o 553 

1 

60 

542819 

60-04 

999735 

.07 

60 • 12 

456916 

0 


Cosine 

D. 

Sine 


Cotang. 

D. 

Tang 


16 


(88 DEGREES.) 






































































20 (2 DEGREES.) A TABLE OF LOGARITHMIC 



M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Colung. 


0 

1 

2 

- 3 

1 1 
6 

7 

8 

9 

ro 

11 

12 

i 3 

U 

1 5 

16 

\l 

19 

20 

21 

22 

23 

24 

2D 

26 

27 

28 

£ 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

Po 

5 1 

52 

53 

54 

55 

56 

^7 

58 

£ 

8-542819 

546422 

549996 

553539 

557054 

j 56 o 54 o 
568999 
567431 
670836 
574214 
677566 

8*580892 

584193 

587469 

690721 

693948 

597162 

6 oo 332 

603489 

606623 

609734 

8-612823 

6x5891 

618987 

621962 

624.965 

627948 

630911 

633854 

636776 

639680 

8-642563 
645428 
648274 
65 1102 
653911 
656702 
659475 
662230 
664968 
667689 

8-670398 
673080 
67675 X 
678405 
681043 
683665 
686272 
688863 
691438 
693998 

8-696543 

699073 

701589 

704090 

706577 

709049 

711507 

713962 

71 6383 
718800 

60-04 

69-55 

59- 06 
58-58 
58 -n 
57-66 
57 -I 9 

56-74 
56 - 3 o 
55-87 
55-44 

55-02 
54 - 60 
54 -19 

53.79 

53.39 

53 -oo 

52 - 6 i 

52-23 

5 1 - 86 
5 i 49 

5 i • 12 

60- 76 
5 o- 4 i 
5 o-o 6 

49-72 

49*38 

49-04 

48 - 7 1 

48-39 

48-06 

47-76 
47-43 
47 • 12 
46-82 
46-52 
46-22 
45-92 
45-63 
45-35 
45 - 06 

44-79 
44 - 5 i 
44-24 
4D97 
43-70 
43 *44 
43 - x8 
42-92 
42-67 
42-42 

42-17 

41 -92 

41 -68 
4 i -44 

41 -21 
40-97 
40-74 
4 o- 5 i 
40-29 
40 -00 

9-999735 

999731 

999726 

999722 

999717 

999713 

999708 

999704 

999699 

999694 

999689 

9-999686 

999680 

999675 

999670 

999665 

999660 

999655 

999650 

999645 

999640 

9-999635 

999629 

999624 

999619 

999614 

999608 

999603 

999697 

999592 

999586 

9-999681 

999675 

999570 

999664 

999558 

999553 

999547 

999541 

999535 

999529 

9-999624 

999618 

999512 

999506 

999500 

999493 

999487 

999481 

999475 

999469 

9-999463 

999456 

999450 

999443 

999437 

99943 i 
999424 
999418 
99941 1 
999404 

! *°7 
! -07 

:3 

1 -08 
•08 
•08 
j -08 
-08 
•08 
; -08 

1 -08 
' -08 

• 08 

• 08 
•08 

• 08 

• 08 
.08 

•°9 

.09 

•oc 

' 

•or 

•09 

.09 

•°9 

•09 

•09 

•°9 

-o 9 

-o 9 

•°9 

•°9 

-o 9 

•°9 

• 10 

. 10 

• 10 

• 10 

• 10 

• 10 

• 10 

-10 

• 10 

• 10 

• 10 

• 10 

-10 

• 10 

• 10 

• 10 

• 11 

• 11 

• 11 

-11 

• 11 

• 11 

• 11 

• 11 

• 11 

• H 

8- 543 o 84 
646691 
55 o 268 
553817 
55 7 336 
560828 
564291 
567727 

! 5 7 ii 3 7 

574620 
577877 

8- 58 1208 
5845 i 4 
687796 

1 691OD1 

594283 
597492 
600677 
6 o 3 S 3 o 
606978 
610094 

8•61 3 189 
616262 
619313 
622343 
625352 
628340 
63 i 3 o 8 
634256 

637184 

640093 

8-642982 
645853 
648704 
65 1537 
654352 

667149 

659928 

662689 

665433 

668160 

8-670870 

673663 

676239 

678900 

681644 

684172 

686784 

689381 

691963 

694029 

8-697081 

699617 

702139 

704646 

707140 

709618 

712083 

7 U 534 

716972 

719396 

60 • 12 
69-62 
69-14 
58-66 
58 -19 
57.73 

67-27 

56-82 

56-38 

55-95 

55-02 

55 -io 
54-68 
54-27 
53-87 
53-47 
53 -08 
52-70 
52-32 
61-94 

5 1 • 08 

5 i - 21 

5 o -85 

5 o- 5 o 

5 o • 1 5 
49-81 
49-47 

49 • 1 3 

48 • 80 
48-48 
48-16 

47-84 

47 * 53 
47-22 
46-91 
46-61 

46 - 3 1 
46-02 
45-73 

40- 44 

45-26 

44-88 

44 - 6 i 

44-34 

44-17 

43 • 80 

43 • 54 
43-28 

43 -o 3 
42-77 
42-52 

42 • 28 

42 -o 3 

41 - 79 
41-55 

4 i -32 

41 -08 

4 o -85 

40-62 

4 o- 4 o 

40-17 

1r-456916 
463309 

449732 

446 i 83 

442664 

489172 

430709 

432273 

428863 

426480 

422123 

11-418792 

415486 

412205 

408949 

405717 

402608 

399823 

396161 

3o3o22 

389906 

ii• 386 S 1 
383738 
380687 
377557 
374648 
371660 
868692 

366744 

362816 

359907 

11-357018 
354147 
361296 
348463 
345648 
34285 i 
340072 
3373 ii 
334567 
33 i 84 o 

11 - 329 i 3 o 
326437 
323761 

321100 

3 i 8456 

3 15828 

3 1 32 16 
310619 

3 08037 
305471 

11 *302919 
3 oo 38 o 
297861 

295354 

292860 | 

290382 

287917 

285465 

283028 

280604 

60 

5 g 

i 58 
! 5 7 
j 56 
• 55 
: 54 
i 53 

52 
: 5 i 
j Do 

12 

47 

1 46 

1 45 

| 44 

43 

42 

4 i 

4 o 

£ 

£ 

35 j 
34 j 
33 ; 
32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 j 
22 ! 
21 

20 

19 

18 . 

l6 

i 5 

14 

i 3 

12 

11 

10 

1 

6 

5 

4 

3 

2 

1 

0 


Cosme 

D. 

Sine 


Cotang. 

D. Tang. 

M. ] 


(87 DEGREES.) 













































































SINES AND TANGENTS. (3 DEGREES.) 


21 


LL 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

--, 

1 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

IC 

11 

12 

1 3 

1 4 

1 5 

16 

\l 

19 

20 

21 

22 

23 

24 

23 

26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

5 0 

5 1 

5 a 

53 

54 

55 

56 

57 

58 

5 9 

60 

8•718800 | 
721204 
723595 
725972 
728337 
730688 
733027 
735354 
737667 
739969 
742269 

8-744536 

746802 

749055 

761297 

753528 

755747 

757955 
76 oi 5 i 
762337 
764611 

8-766675 
768828 
770970 
773101 
775223 
777333 
779434 
'tS 1 524 
7 S 36 o 5 
785675 

8-787736 

789787 

791828 

793809 

795881 

797894 

799897 

801892 

803876 

8 o 5852 

8-807819 

809777 

811726 

813667 

815599 

817622 

819436 

82 i 343 

823240 

825 i 3 o 

8-827011 

828884 

830749 

832607 

834456 

836297 

838 i 3 o 

839956 

841774 

843585 

4 o-o 6 

39-84 

39-62 

39-41 

39-19 

38 .98 
38-77 
38-57 
38-36 
38 -16 
37-96 

37-76 

37-56 

37-37 

37-17 

36-98 
36-79 
36 - 6 i 
36-42 
36-24 
36 -06 

35-88 

35-70 

35-53 « 

35-35 

35 -i 8 

35 -oi 

34-84 

34-67 

34 - 5 1 
34 - 31 

34 -18 
34-02 
33-86 
33-70 
33-54 
33.39 
33-23 
33 -o 8 
32-93 
32-78 

32-63 

32-49 

32-34 

32-10 

32-00 

3 i -91 

3 1 • 77 

3 1 - 63 

3 1 • 49 

3 1 - 35 

3 l -22 

3 i - 08 
3 o-o 5 
3 o -82 
30-69 
3 o -56 
3 o -43 
3 o- 3 o 
3 o-17 
3 o-oo 

9-999404 
999398 
999391 
999384 
999378 
99937i 
999364 

999357 

999350 

999343 

999336 

9-999329 

999322 

999815 

999308 

999301 

999294 

999286 

999279 

999272 

999260 

9.999257 

999260 

► 999 2 4 ? 

999230 
999227 
999220 
999212 
999205 
999197 

999 i8 9 

9.999181 

999 1 74 
999166 
9991 58 
9991 5 o 
999142 
999134 

999126 
999118 
999110 

9-999102 

999094 

999086 

999077 

999069 

999061 

999053 

999044 

999036 

999027 

9 - 999 oi 9 

999010 
999002 
998993 
998984 

998976 

998967 

998968 

998950 

998941 

• 11 

• 11 

• 11 

• 11 

• 11 

• 11 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• 12 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 
-13 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 

• i 3 
-13 

• i 3 

• 14 
•14 

• 14 

• 14 

• 14 

• 14 

• 14 
•14 
•14 

.14 

• 14 
•14 
•14 
•14 

• 14 

• i 5 

• i 5 

• i 5 

• i 5 

8-719396 
721806 
724204 
726588 
728959 
731 3 17 
733663 
735996 
7383 i 7 
740626 
, 7429.22 

8-740207 

747479 

749740 

751989 

754227 

756453 

758668 

760872 

763 o 65 

766246 

8-767417 

769578 

771727 

773866 

773995 

778114 

780222 

782320 

784408 

786486 

8-788554 

790613 

792662 

794701 

796731 

798752 

800763 

802765 

804768 

806742 

8-808717 

8 io 683 

812641 

814689 

816629 

8i8461 
820384 

822298 

824206 

826103 

8-827992 

829874 
831748 
8336 i 3 
835471 
837321 
839163 
840098 
842826 
844644 

40-17 
39-95 i 
39-74 i 
39-52 1 

39 * 3 o 
39-09 

ih 

38-48 

38-27 

38-07 

37-87 

37-68 

37.49 

37-29 
37-10 
36-92 
36-73 
36-55 
36-36 
36 -18 

36 -oo 

35-83 

35-65 

35-48 

35 - 3 i 

35 -i 4 

34-97 

34 - 8 o 

34-64 

34-47 

34 - 3 1 
34-15 

33-99 

33-83 

33-68 

33-52 

33-37 

33-22 

33-07 

32-92 

32-78 
32-62 
32-48 
32-33 
32 - 1<2 
32 -o 5 
31-91 

3 1 *77 

3 1 - 63 
3 i- 5 o 

3 1 - 36 

3 1 • 23 

3 i • 10 
30-96 
3 o -83 
30-70 
3 o -57 
3 o -45 
3 o -32 
3 o-19 

11•280604 
278194 
276796 
273412 
271041 
268683 
266337 
264004 
26 i 683 

259374 

267078 

1i-264793 
262621 
260260 
248011 
246773 
243547 

241332 
239128 
236935 
234754 

11 •232583 
23 o 422 

228273 

226134 

224006 

221886 

219778 

217680 

215592 

2 i 35 i 4 

11•211446 

209387 

207338 

206299 

203269 

201248 

199237 

197235 

196242 

193268 

11-191283 

189317 

187359 

185411 

183471 

181 539 
179616 
177702 
176795 
173897 

11-172008 
170126 
168262 
166387 
164629 
162679 
160837 
169002 
167176 

1 55356 

60 

69 

58 

5 ) 

56 

55 

54 

53 

D2 

5 i 

5 o 

49 ! 

48 | 
47 

46 

45 

44 

43 

42 

4 i 

4 o 

3 9 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

1 9 

18 

1 17 
l6 

i 5 

i 4 

i 3 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 


Cosine 

D. 

Sine 


Cotang. 1 D. 

Tang. 

M. 


(86 DEGREES.) 













































































22 


(4 DEGREES.) A TABLE OF LOGARITHM]"G 


|M. 

Sine 

D. 

Cosine 

D. 

0 

1 

2 

3 

i 

6 

7 

8 

9 

10 

11 

12 

1 3 

14 

1 5 

16 

1 1 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

3 0 

3 1 

32 

33 

34 

35 

36 

U 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

£ 

5 1 

52 

53 

54 

55 

56 

ll 

8-843585 
845387 
847183 
848971 
860761 
852525 
854291 
856 o 49 
857801 
859546 
861283 

8 - 863 oi 4 
864738 
866455 
8681 65 
869868 
871665 
873255 
874938 
876616 
878285 

8-879949 

881607 

883258 

884903 

886542 

888174 

889801 

891421 

8 9 3 o 35 

894643 

8-896246 

897842 

899432 

901017 

902596 

904169 

906736 

907297 

908853 

910404 

8-911949 

913488 

916022 

9 i 655 o 

918073 

919691 

921103 

922610 

924112 

925609 

8-927100 
928587 
930068 
931544 
933 oi 5 
934481 
935942 
937898 
938860 
940296 

3 o-o 5 

29-92 

29-00 

29-67 

29*55 

29-43 

29-31 

29-19 

29-07 

28-96 

28-84 

28-73 
28-61 
28 • 5 o 
28-39 
28-28 
28-17 
28-06 
27-96 
27 • 86 
27.73 

27-63 
27-52 
27-42 
27 • 3 1 
27-21 
27-11 
27-00 
26-90 
26-80 
26-70 

26-60 

26-61 

26-41 

26 - 3 i 
26-22 
26-12 
26-o 3 
25- 9 3 

25 - 84 

26- 75 

25-66 

25-56 

25-47 

25-38 

25-29 
25-20 
25-12 
25 -o 3 

24-94 

24-86 

24-77 
24-69 
24-60 
24-52 
24-43 
24-35 
24-27 
24-19 
24-1 1 
24 -o 3 

9-998941 

998932 

998923 

998914 

998905 

998896 

998887 

998878 

998869 

998860 

998861 

9-998841 

998832 

998823 

998813 

998804 

998795 

998785 

998776 

998766 

998767 

9-998747 

998738 

998728 

998718 

998708 

998609 

998689 

998679 

998669 

998659 

9-998649 

998639 

998629 

998619 

998609 

998599 

998689 

998678 

998568 

998558 

9-998548 

998537 

998627 

998516 

998606 

998496 

998485 

998474 

998464 

998453 

9-998442 

998431 

998421 

998410 

998399 

998388 

998377 

998366 

998355 

998344 

• i 5 

• i 5 

• i 5 
•i 5 

• i 5 

• i 5 

• i 5 

• i 5 

• i 5 

• i 5 

• i 5 

-15 

• i 5 

• 16 
| • 16 

‘"a 
<■ 16 

• 16 

• 16 

• 16 

• 16 

• 16 

• 16 

• 16 

• 16 

• 16 

• 16 
•16 

• 16 
•17 
•17 

•H 

•17 

•17 

•n 

-17 

•17 

•17 

•17 

•17 

-17 

•17 

-17 

•n 

•18 

•18 

• 18 
•18 
•18 
•18 
•18 

• 18 

• 18 

• 18 
•18 
•18 
•18 

• 18 

• 18 
.18 

• 18 

1 Cosine 

D. 

Sine 






. ■ ■ 

Tang. 

D. 

Cotang. 


8-844644 

3 o-19 

11 • 1 55356 

60 

846455 

30-07 

i 53545 

5 9 

848260 

29-96 

161740 

58 

860067 

861846 

29-82 

29-70 

149943 

148154 

57 

56 

853628 

29.58 

146372 

55 

8554 o 3 

29-46 

144597 

54 

867171 

29-35 

142829 

53 

868932 

29-23 

141068 

I 52 

860686 

29-11 

139814 

5 i 

862433 

29-00 

137567 

5 o 

8-864173 

28-88 

11-135827 

49 

866906 

28-77 

134094 

48 

867632 

28-66 

132368 

47 

869351 

28-54 

130649 

46 

871064 

28-43 

128936 

45 

872770 

28-32 

127230 

44 

874469 

28-21 

1 2553 1 

43 

876162 

28-11 

123838 

42 

877849 

28-00 

1221 5 1 

4 i 

879629 

27-89 

120471 

4 o 

8-881202 

27-79 

11•118798 

39 

882869 

27-68 

1171 3 1 

38 

884530 

27-58 

118470 

37 

8861 85 

27-47 

n 38 i 5 

36 

887833 

27-37 

112167 

35 

889476 

27-27 

1io 524 

34 

891112 

27-17 

108888 

33 

892742 

27-07 

107258 

32 

894366 

26-97 

io 5634 

3 i 

896984 

26-87 

104016 

3 o 

8-897696 

26-77 

11 •102404 

29 

899203 

26-67 

100797 

28 

900803 

26-58 

099197 

27 

902398 

26-48 

097602 

26 

903987 

905570 

26-38 

09601 3 

25 

26-29 

094430 

24 

907147 

26 • 20 

092853 

23 

908719 

26-10 

091281 

22 

910285 

26-01 

089715 
088154 | 

21 

911846 

25-92 

20 

8-913401 

25-83 

i1•086099 

IO 

914961 

916496 

25-74 

25-65 

086049 

o 835 oO 

I8 

17 

918034 

25-56 

081966 

l6 

919568 

25-47 

080432 

i 5 

921096 

25-38 

078904 

14 

922619 

25 - 3 o 

077881 1 

i 3 

924136 

25-21 

076864 ] 
074351 ! 

12 

925649 

25-12 

11 

927156 

25 -o 3 

072844 

10 

3-928658 

24-95 

11 071342 

q 

93 oi 55 

931647 

24-86 

24-78 

069845 

068353 

7 

933 1 34 

24-70 

066866 

6 

934616 

24-61 

065384 

5 

936093 

24-53 

063907 

4 

937665 

24-46 

062435 

3 

939032 

24-37 

060968 

2 

940494 

941902 

24 - 3 o 

24-21 

069006 

o 58 o 48 

1 

0 

Cotang. 

D. 

Tang. 

M. 


(85 DEGREES.) 












































































SINES. AND TANGENTS. (5 DEGREE.) 


23 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

0 

8*940296 

24-o 3 

9-998344 

.19 

8-941952 

24-21 

11-068048 

60 

i 

941738 

23-94 

998333 

.19 

943404 

24-13 

066596 

5 9 

2 

943 i 74 

23-87 

998322 

•19 

944852 

24 *o 5 

o 55 i 48 

58 

3 

944606 

23-79 

998311 

•19 

946296 

23.97 

053706 

57 

4 

946034 

23-71 

998800 

-19 

947734 

23*90 

052266 

56 

5 

947456 

23-63 

998289 

-i 9 

949168 

23-82 

o 5 o 832 

55 

6 

948874 

23-55 

998277 

-19 

950697 

23-74 

049403 

54 

7 

960287 

23-48 

998266 

-i 9 

952021 

23-66 

047979 

53 

8 

961696 

23 -4o 

998255 

* 1 9 

953441 

23 -6o 

046669 

62 

9 

963100 

23-32 

998243 

• 19 

964856 

23 - 5 j 

o 45 i 44 

5 i 

10 

964499 

23-25 

998232 

.19 

966267 

23 • 44 

043733 

5 o 

ii 

8-955894 

23-17 

Q•Q9822O 

•19 

8-967674 

23-37 

11-042326 

49 

12 

997284 

23-10 

998209 

•19 

969076 

23-29 

040925 

48 

i 3 

908670 

23-02 

99 8l 97 

.19 

960473 

23-23 

039627 

47 

14 

960052 

22-05 

998186 

•19 

961866 

23 • 14 

o 38 i 34 

46 

i 5 

961429 

22-88 

998174 

.19 

963255 

23*07 

036745 

45 

16 

962801 

22-80 

998163 

.19 

964639 

23-00 

o 3536 i 

44 

l 7 

964170 

22-73 

998151 

.19 

966019 

22-93 

033981 

43 

18 

965534 

22-66 

998139 

• 20 

967394 

22-86 

032606 

42 

l 9 

966898 

22-59 

998128 

• 20 

968766 

22-79 

o 3 i 234 

4 i 

20 

968249 

22-52 

998116 

•20 

970133 

22-71 

029867 

40 

21 

8-969600 

22-44 

9-998104 

• 20 

8-971496 

22-65 

11-o285o4 

3 9 

22 

970947 

22-38 

998092 

• 20 

972835 

22-67 

027145 

38 

23 

972289 

22 -3 I 

998080 

• 20 

974209 

22 • 5 l 

026791 

37 

24 

973628 

22-24 

998068 

• 20 

975560 

22-44 

024440 

36 

25 

974962 

22 • 17 

998066 

• 20 

976906 

22-37 

023094 

35 

26 

976298 

22 • IO 

998044 

• 20 

978248 

22 - 3 o 

021762 

34 

27 

977619 

22 -o 3 

998082 

• 20 

979086 

22-23 

020414 

33 

28 

978941 

21-97 

998020 

• 20 

980921 

22-17 

019079 

32 

2 9 

980269 

21-90 

998008 

• 20 

982261 

22- 10 

017749 

3 i 

3 o 

981678 

21-83 

997996 

• 20 

983577 

22-04 

016428 

3 o 

3 i 

8-982883 

21.77 

9-997985 

• 20 

8 • 984899 

21.97 

11-oi 5 ioi 

29 

32 

984189 

21-70 

997972 

• 20 

986217 

21 -91 

013783 

28 

33 

985491 

21-63 

997969 

• 20 

987532 

21-84 

012468 

27 

34 

986789 

21-67 

997947 

• 20 

988842 

21-78 

ox 11 58 

26 

35 

988088 

21-50 

997985 

• 21 

990149 

21 * 7 * 

009891 

25 

36 

989374 

21-44 

997922 

• 21 

99:431 

21 -65 

008649 

24 

3 7 

990660 

21 -38 

997910 

• 21 

992760 

21-58 

007250 

23 

38 

991943 

21 - 3 1 

997897- 

• 21 

994040 

21-52 

006955 

22 

3 9 

993222 

21-25 

997883 

• 21 

993887 

21-46 

004663 

21 

4 o 

994497 

21-19 

997872 

• 21 

996624 

21-40 

003376 

20 

4 i 

8-995768 

21 • I 2 

9-997860 

• 21 

8-997908 

21-34 

11-002092 

*9 

42 

997086 

2 1 • 06 

997847 

• 21 

999188 

21-27 

0008i2 

18 

43 

998299 

21-00 

997833 

• 21 

9-000465 

21-21 

10-999936 

i 7 ' 

44 

999560 

20-94 

997822 

• 21 

001788 

2 I • I 5 

998262 

16 

45 

9•0008i6 

20-87 

997809 

• 21 

003007 

21-09 

996998 

i 5 


002069 

20-82 

997797 

•21 

004272 

21 - o 3 

995728 

14 

47 

oo 33 i 8 

20-76 

997784 

• 21 

oo 5534 

20'97 

994466 

i 3 

48 

004563 

20-70 

997771 

• 21 

006792 

20 -QI 

993208 

12 

49 

oo 58 o 5 

20-64 

997708 

•21 

008047 

20-85 

991953 

11 

5 o 

007044 

20-58 

997743 

• 21 

009298 

20- 80 

990702 

10 

5 i ; 

9-008278 

20-52 

9-997782 

• 21 

9-010546 

20-74 

10-989454 

9 

52 

009610 

20-46 

997719 

•21 

011790 

20-68 

988210 

8 

53 

010737 

2 o- 4 o 

997706 

•21 

oi 3 o 3 i 

20-62 

986969 

7 

54 

011962 

20-34 

997693 

• 22 

014268 

20-56 

985732 

6 

55 

01 3 182 

20-29 

997680 

•22 

oi 55 o 2 

20 - 5 l 

984498 

5 

56 

014400 

20-23 

997667 

•22 

016732 

20-45 

983268 

4 

5 7 

oi 56 i 3 

20-17 1 

997654 

•22 

017939 

20-40 

982041 

3 

58 

016824 

20-12 

997641 

• 22 

019183 

20-33 

980817 

2 

5 g 

ci 8 o 3 i 

20-06 

997628 

• 22 

O 2 o 4 o 3 

20-28 

970597 

1 

60 

019235 

20-00 

997614 

•22 

021620 

20-23 

978380 

0 

1 

1 

! 

Cosine ! 

D. ! 

Sine 1 

! Cotang. 

_S._ 

D. 

Tang. 

M. 

-< 


(84 DEGREES.) 





























































24 


(6 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang, j D. 

Cotang. 

1 

0 

1 

2 

3 

4 

5 

1 ^ 
i 7 

8 

9 

10 

11 

12 

i3 

*4 

10 

16 

17 

18 

*9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

30 

31 

32 

33 

34 

35 

36 

37 

38 

3 9 

40 

41 

42 

43 

44 

45 

46 

47 

48 

l 49 

| 5o 

f 5i 

f 52 

1 53 

I 64 
55 
f 56 

I 57 
! 5S 

1 9 

60 

9-019235 

020435 

021682 

022826 

024016 

025203 

026386 

027567 

028744 

029918 
o31089 

9-o32257 

o3342i 

084682 

o3574i 

086896 

o38o48 

039197 

o 4 o 342 

o 4 i 485 

042625 

9-043762 
044895 
046026 
047154 
048279 
049400 
o 5 o 5 iq 
o 5 i 63 o 
052749 
o 53859 

9•054966 
066071 
05-7172 
068271 
059367 
060460 
061551 

062639 

063724 

064806 

9-o65885 
066962 
o68o36 
069107 
070176 
071242 
072306 
073366 
074424 
076480 

9-076533 
077583 
078631 
079676 
080719 
! 081769 

082797 

1 083832 

| 084864 

086894 

1 

20-00 

19-95 

19-89 

I9-84 

19-78 

19.73 

i 9' 6 7 

19-62 

i 9 - 5 7 

19-61 

19.47 

19-41 

19-36 
i9-3o 
19-25 
19-20 
19-15 
19-10 
19 -o 5 
io*99 
18-94 

18-89 

18-84 

18-79 

18-75 

18-70 

18 - 65 

18-6o 
i8-55 
i8-5o 
i 8-45 

18-41 

1S • 36 
i 8-3 i 
18-27 
18-22 
18-17 
18-i 3 

18-08 
18-04 
*7-99 
17-94 

17 *£ 

17-86 

17-81 

n-n 

17.72 

17 -68 
17-63 
l V 5 n 

17-5 d 

17-60 

17-46 

17-42 

17-38 

17-33 

17-29 

17-26 

17-21 

17-17 

17 • i3 

9-997614 

997601 

997688 

997674 

997661 

997547 

997534 

997620 

997507 

9974 q 3 

997480 

9-997466 

997402 

997439 

997426 

997411 

997397 

997383 

997369 

997355 

997841 

9-997327 

9973 i 3 

697299 

997280 

997271 

997257 

997242 

997228 

997214 

997199 

9•997 1 85 
997170 
997106 

997141 

997127 

997112 

997098 

997083 

997068 

997053 

9'997 0 39 
997024 
997009 

996994 

996979 

996964 

996949 

996934 

996919 

996904 

9•996889 

996874 

996868 

996843 
996828 
996812 
996797 
996782 
996766 
996761 

• 22 

• 22 

• 22 

-22 . 

•22 

•22 

•23 

•23 

-23 

•23 

•23 

•23 

•23 

-23 

•23 

•23 

-23 

-23 

•23 

-23 

-23 

.24 

•24 

•24 

• 24 
•24 
•24 

• 24 
•24 
•24 

• 24 

•24 

•24 

•24 

•24 

•24 

•24 

•24 

•25 

•25 

•25 

•25 

•25 

•25 

•25 

•25 

•25 

-25 

•20 

•25 

•25 

•25 

•25 

•25 

•25 

•25 

• 26 

• 26 

• 26 

• 26 

• 26 

9-021620 

022834 

024044 

02525 i 

026455 

027655 

028852 

080046 

o3i237 

o 32425 

033609 

9-034791 
035969 
037144 
o383i6 
039485 
040601 
041813 
042973 
04413o 
045284 

9-046434 

047682 

048727 

049869 

o5ioo8 

o52i44 

053277 

054407 

o55535 

066659 

9-057781 
058900 
060016 
061i3o 
062240 
063348 
064453 
o65556 
o66655 
067752 

9-068846 
06993S 
071027 
072113 
073197 
074278 
075356 
076432 
077005 
078676 

9-079644 

0S0710 

081773 

082833 

083891 

084947 

086000 

087060 

088098 

089144 

20-23 

20-17 

20-11 

20-06 
20-00 

!9-9 5 

19-90 

19*80 

19-79 

19.74 

19.69 

19-64 

19-53 

19-53 

19-48 

19-43 

19-38 

19*33 

19-28 

19-23 

19-18 

19* i3 
19-08 
19-03 

18-98 

i 8- 9 3 

18-89 

18-84 

18.79 

18-74 

18-70 

18 • 65 
18-69 
i8.55 

18 • 5i 
18-46 
18-42 
18-37 
18-33 
18*28 
18-24 

18-19 
18-10 
18-10 
18-06 
18-02 
17-97 
17-93 
17-89 
17-84 
17-80 

17-76 

17.72 

17-67 

17-63 

17-69 

17-55 

17 - 5i 

17.47 

17*43 

17-38 

10-978380 ; 
977166 
976966 
974749 
97354- 1 
972345 
971148 
969954 , 
968763 
96757O 
966391 

10-965209 
964031 
962856 
961684 
960515 

909349 

958187 

957027 

955870 

954716 

io -953566 

962418 

961273 

95 oi 3 i 

948992 

947806 

946723 

9455g3 

944465 

948341 

10-942219 
941100 
989984 
938870 
987760 
936652 
935547 

984444 

933345 

932248 

10•931154 
930062 
928973 
927087 
926803 
925722 
924644 
923568 
922495 
921424 

10-920356 

919290 

918227 

917167 

916109 

915o53 
914.000 
912960 
911902 
910856 

60 

5 9 

58 

5? 

56 

55 

54 

53 

5 a 

5i 

5o 

49 

48 

47 

46 

45 

44 

43 

43 

4i 

40 

3a 

38 

37 

36 

35 

34 

33 

32 

3i 

3o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

j 5 

14 

i3 

12 

11 

10 

7 

6 

5 

' 4 

3 

2 

1 

0 

I Cosine 

D. 

Sine 

Cotang. 

D. 

Tang. 

_su___ 

M. 


^83 DEGREES.) 






























































SIKES AND TANGENTS. (7 DEGREES.) 


9' 


M. 


o 

i 

3 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

L 9 

31 

32 

33 

34 

35 

36 
3 
3 

3 9 

40 

41 

42 

43 

44 

45 

46 

47 
43 

S 

51 

52 , 

53 ! 

54 J 

•55 
56 I 
5: 

58 

£ 

bo 


Sine 


D. 


9-085894 
086922 
087947 
088970 
089990 
091008 
092024 j 
093037 j 
094047 ; 
095o56 
096062 j 

9-097065 j 
098066 
099065 
100062 
ioio 56 
102048 
io 3 o 37 
io 4 o 25 
io 5 oio 
106992 

9-106973 
107961 
108927 
10990i 

110873 

111842 
112809 

11 3774 
114737 
115698 

9-11 6656 
117613 
118567 
119519 
120469 
121417 
122362 
i 233 o 6 
124248 
126187 

9-126125 
127060 
127993 
128925 
129804 
130781 
131706 
i 3263 o 
1 3355 1 

134470 

9 -i 35387 
i 363 o 3 
137216 
138128 
139037 
139944 
i 4 o 85 o 
141754 
142655 
143555 


17 • i3 
17.09 

17-04 
17-00 
16-96 
16-92 
16-88 
16-84 
16-80 
16-76 
16-73 

16-68 
i6-65 
16-61 
16-57 
16 -53 
16-49 
16-46 
i 6-4 i 
i 6-38 
16-34 

i6-3o 
16-27 
16 • 23 
16-19 
16 • 16 
16-12 
16-08 
i6-o5 
16 -oi 
✓ io -97 

1 5 - 94 

16- 90 
16-87 
15 - 83 
i5-8o 

15- 76 
1 5 - 73 

16- 69 
15 -66 
i 5-62 

15 - 59 
i5-56 
10-52 

15.49 
15 • 40 
i 5-42 
15 • 3g 
i 5-35 
i 5-32 
10-29 

15 - 25 
1 5 • 22 
15 • 19 
15 • 16 
1 5 • 12 
t 5-09 
i 5 -o 6 
i5-o3 
15 -oo 
14-96 


Cosine 


9-996751 

996735 

996720 

996704 

996688 

996673 

996657 

996641 

996625 

996610 

996694 

9-996578 
996662 
996546 
996530 
996614 
996498 
996482 
996465 
996449 
996438 

9-996417 

996400 

996384 
996368 
996351 
996335 
996318 
996302 
996285 
996269 

i 9-996262 
996230 
996219 
996202 
996i85 
996168 
996151 

996134 

996117 

996100 

9•996083 
996066 
996049 
996032 
996015 
996998 
996980 
995963 
996946 
996928 

9-996911 

990894 
996876 
996869 
996841 
996828 
995806 
996788 
990771 
996763 


D. 


•26 

•26 

• 26 
•26 

• 26 

• 26 
•26 

• 26 
•26 
•26 

• 26 

.27 

.27 

.27 

• 27 
.27 
.27 

•27 

•27 

• 27 

•27 

•27 

•27 

-27 

•27 

•27 

•27 

•27 

• 28 
-28 
-28 

• 28 

• 28 
.28 

• 28 

• 28 
•28 

• 28 

• 28 
-28 
•28 

•29 

•29 

•29 

•29 
•29 
•29 
•29 j 
•29 | 
•29 

• 29 

• 29 

•29 

-29 
.29 

•29 

• 29 

•29 
•29 
•29 
■29 


Tang. 


D. 


Cosine 


D. 


Sine 


1 


9-089144 

090187 

091228 

092266 

093302 

094336 

095367 

096395 

097422 

098446 

099468 

9-100487 

ioi 5 o 4 

102619 

io 3532 

104642 

io555o 

io6556 

107559 

io856o 

109559 

9 -iio 556 
iii 55i 

112643 
n3533 
ii 452 i 
u 55 o 7 1 
116491 - 
117472 
118402 j 

II9429 ! 

I 

9-120404 j 
1 2 l 377 I 
122348 j 
123317 
124284 | 
126249 
126211 ; 
127172 J 
I28 i 3 o 1 
129087 | 

q-i 3 oo 4 i , 

130994 | 
131944 | 
132893 | 

13383 9 j 
134784 j 
135726 j 
136667 j 
i 376 o 5 
i 38542 j 

9•139476 I 
140409 1 
i 4 i 34 o | 
142269 
143196 
i 44 i21 
146044 
146966 
146885 
147803 

Cotang. 


Cotang. 


] 


17-38 
17*34 
n-3o 
17-27 
17-22 

17*19 

17 * 15 
17-11 
17-07 
17-o3 

16-99 

16-96 
16-91 
16-87 
16-84 
16-80 
16-76 
16-72 
16-69 
i6-65 
16 • 61 

i6-58 
i6-54 
i6-5o 
16-46 
16-43 
16-39 
16 -36 
i6-32 
i6- 29 
16-20 

16- 22 
16 • 18 
16 -15 
16 • f x 
16-07 
16-04 
16-01 
15.97 
10-94 

15- 91 

16- 87 
16-84 
15 • 81 

16-77 

16-74 

15 • 71 
16-67 
15 • 64 
15 • 61 
i5-58 

15 • 55 
15 • 51 
15 • 48 
15 - 45 

15- 42 

16- 39 
15 - 3 o 
15 • 32 
r5 • 29 
16-26 

D. 


ic-9io856 ; 60 
900813 5c 
908772 58 

907734 67 
906698 1 56 
906664 55 

904633 64 

9 o 36 o 5 53 

902678 52 

901554 5i 
900032 5o 

10-899613 49 

898496 48 

897481 47 

896468 46 

896468 45 

894460 44 

893444 43 

892441 42 

891440 41 

890441 40 

10-889444 ! 39 
888449 38 

887467 37 

886467 36 

880479 35 

884498 34 

883509 ; 33 
882528 : 32 
881548 j 3i 

880671 j 3o 

10-879696 
878623 
877652 
876683 

876716 
874761 
873789 
872828 
871870 
870913 

10-869969 
869006 
868 o 56 
867107 
866161 
866216 
864274 
863333 
862395 
861408 

io-86o524 
869691 
85866 o 
807731 , 

866894 
855879 
804.956 
804084 
853 11 5 
862197 

Tang. 


29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

10 

! 7 

lb r 

i5 

14 

i3 

1 2 

11 
10 

8 

7 

6 

5 

4 

3 

2 

i 

o 

mT ! 


(82 DEGREES.) 







































































































CT'OtOtOtOiOtCTtUtCOtUt u< ix 4x *. ix ix Jx 4 x ix +x ^WWCoWWOJWWW Ojummwiokikjmu »oi—i>—i»—<*-*i—<>—<»— ii—i>—« I— 

o 0 POO O' COt*. Go to — O O COO O' Oi*. WW H O O COO O' Ot*« Co to *- OO QO—J O' Crt*. Co to -■ O O 00-0 O' COt*. Co to — O O t* 0 O' Otix CO to 


26 


(8 DEGREES.) A TABLE OF LOGARITHMIC 


M. 


o 

I 


Sine 


9 *143555 
144453 

145349 
146243 
i47i36 
148026 
148916 
149802 
15o686 
151069 
152451 

9-i5333o 
154208 
i55o83 
155967 
i5683o 
157700 
158569 
159435 
i 6 o 3 oi 
161164 

9-162025 
162885 
163743 
164600 

166464 
166307 
167169 
168008 
168856 
169702 

9-i7o547 
171389 
172230 
173070 
173908 
174744 
175578 
176411 
177242 
178072 

9-178900 

179726 

i8o55i 

181374 

182196 

i83oi6 

183834 

184661 

185466 

186280 

9-187092 
187903 
188712 
189519 
190329 
191130 
191933 
192734 
193534 
194332 


D. 


Cosine 


14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

i4 
14 

14 

i4 

14 

U 

14 

14 

14 

U 

14 

14 

14 

14 

14 

14 

14 

14 

14 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 

i3 


96 

9 3 
90 

87 

84 

81 

78 

75 

72 

69 

66 

63 

60 

5 7 

54 

5i 

48 

45 

42 

3 9 

36 

33 

3o 

27 

24 

22 

*9 

16 

i3 

10 

07 

o5 

02 

99 

96 

94 

1 


86 

83 

80 

77 

74 

72 

69 

66 

64 

61 

5 9 

56 

53 

5i 

48 

46 

43 

41 

38 

36 

33 

3o 

28 


Cosine 


9-995753 

996735 

996717 

995699 

995681 

996664 

996646 

996628 

996610 

996691 

996673 

9-995555 

995537 

996619 

9955 oi 

995482 

996464 

996446 

996427 

990409 

995390 

9-996372 

995353 

995334 

995316 

996297 

996278 

996260 

995241 

995222 

996203 

9-995184 

996166 

996146 

996127 

996108 

996089 

996070 

996061 

995 o 32 

995 oi 3 

9-994993 

994974 

9949:16 

994935 
994016 
994896 
994877 
994807 
994838 
994818 

9-994798 

994779 

994709 

994739 

994719 

994700 

994680 

994660 

994640 

994620 


D. 


Sine 


D. 


3o 

3o 

3o 

3o 

3o 

3o 

3o 

3o 

3o 

3o 

3o 

3o 

3o 

30 

31 
3i 
31 
3i 
31 
3i 
3i 

3i 

3i 

3i 

3i 

3i 

3i 

31 

32 
32 
32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

33 
33 
33 
33 
33 
33 

33 

33 

33 

33 

33 

33 

33 

33 

33 

33 


Tang. 


9-147803 
148718 
149632 
15 o 544 
i 5 i 404 
152363 
153269 
104174 
155077 
155978 
166877 

9-157775 
158671 
169565 
160457 
161347 
162236 
i63123 
164008 
164892 
165774 

9- i 66654 

167532 

168409 

169284 

170157 

171029 

171899 

172767 

173634 

174499 

9-175362 

176224 

177084 

177942 

178799 

179660 

i8o5oS 

i8i36o 

182211 

183069 

9•183907 
184762 
185597 
186409 
187280 
188120 
i 88 9 58 
189794 
190629 
191462 

9-192294 
193124 
193953 
194780 
196606 
196430 
197253 
198074 
198894 
199713 


D. Cotang. 


Cotiing. 


i 5 

i 5 

i 5 

i 5 

i 5 

i 5 

i 5 

i 5 

i 5 

14 

14 

14 

14 

14 

14 

14 

14 

14 

U 

14 

14 

14 

14 

14 

14 

14 

U 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

14 

i 3 

i 3 

i 3 

i 3 

i3 

i 3 

i 3 
i 3 
i 3 
i 3 
13 
i 3 
i 3 
i 3 
i 3 
i 3 


26 

23 

20 

17 

14 

11 

08 

o5 

02 

99 

96 

93 

9° 

84 

81 

79 

76 

73 

70 
67 

64 

61 

58 

55 

53 

5o 

47 

44 

42 

3 9 

36 

33 

3i 

28 

25 

23 

20 

17 

1 5 

12 

°9 

07 

04 

02 

99 

96 

93 

1 

84 

81 

79 

76 

74 

71 
69 
66 
64 

61 


10-852197 

861282 

85o368 

849456 

848646 

847637 

846731 

845826 

8449^3 

844022 

843 i 23 

10-842225 

841329 

84 o 435 

83 9 543 


837764 
836877 
835992 
835108 
834226 

10-833346 
832468 
831691 
830716 
829843 
828971 
828101 
827233 
826366 
8255 oi 

10-824638 

823776 

822916 

822058 

821201 

82 o 345 

819492 

818640 

817789’ 

816941 

10-816093 
816248 
8i44o3 
81356i 
812720 
811880 
811042 
810206 
809371 
8o8538 

10-807706 

806876 

806047 

8 o 5220 

804394 

803570 

802747 

801926 

801106 

800287 


D. 


Tang. 


60 


7 

6 

5 

4 

3 

St 

1 

o 

M. i 


(81 DEGREES.) 


to to to to to to to to to to ooCoCjcocooocoCooogo *.*'*'*'*'*'*.*'*'*. oioiututotyiotoiotot 
o to CO*. cj< O'J COO O "" to Co*. OtO-J COO O to Go*' OtO'-J OOO O — to Go*. O'-^l COO O “■ to Co*. tji O'J OCO 




























































SINES AND TANGENTS. (9 DEGREE.) 27 


M. 

Sine 

D. 

Cosine 

D. 

Tang,. 

D. 

Cotang. 


0 

9 -194332 

i 3-28 

9-994620 

• 33 

9 *i 997 i 3 

1 3 • 61 

r 

CO 

CM 

O 

O 

CO 

0 

60 1 

i 

195129 

i 3-26 

994600 

-33 

200629 

i 3 - 5 9 

799471 

l | 

5 g 

2 

I 9 5 9 20 

1 3 • 23 

99 458 o 

•33 

201345 

1 1 3•56 

798655 

58 

3 

196719 

1 3 • 2 x 

99 456 o 

* 3 4 

2021 5 9 

1 3 • 54 

797841 

5 t 

4 

197611 

1 3 • 18 

994540 

•34 

202971 

i 3 -52 

797029 

56 

5 

i 9 83 o 2 

1 3 • 16 

9 9 45 i 9 

•34 

203782 

1 3 • 49 

796218 

55 

6 

199091 

i 3-13 

994499 

•34 

204692 

1 3 • 47 

795408 

54 

7 

199879 

1 3 • 11 

994479 

• 34 

205400 

1 3 - 45 

794600 

53 

8 

200666 

1 3 -08 

99445 c 

• 3 4 

206207 

1 3 -42 

793793 

52 

9 

201421 

1 3 -06 

994438 

*34 

207013 

i 3 - 4 o 

792987 

1 51 

10 

202234 

i 3 -o 4 

994418 

•34 

207817 

i 3-38 

792183 

j 5 o 

11 

9 -2o3oi7 

i 3 -oi 

9-994397 

•34 

9-208619 

i 3-35 

10-791881 

i 4 9 

12 

203797 

12 '99 

994377 

•34 

209420 

i 3-33 

790580 

48 

i 3 

204577 

12-96 

994357 

•34 

210220 

1 3 - 3 1 

789780 

47 

14 

205354 

12-94 

994336 

•34 

211018 

1 3 • 28 

788982 

46 

i 5 

2061 3 1 

1 2 ' 9 2 

9943 16 

•34 

21181 5 

1 3 • 26 

788185 

45 

16 

206906 

12-89 

99 42 9 5 

•34 

212611 

i 3-24 

787389 

44 

l l 

207679 

12-87 

994274 

•35 

2 i 34 o 5 

1 3 • 21 

786095 

43 

18 

208422 

12-85 

994264 

•35 

214198 

i 3 -19 

785802 

42 

*9 

209222 

12-82 

994233 

•35 

214989 

i 3 -17 

78501I 

4 i 

20 

209992 

12-8o 

994212 

•35 

210780 

i 3 • 1 5 

784220 

40 

2 I 

9-210760 

12-78 

9-994191 

-35 

9 - 2 i 6568 

1 3 -12 

10-783432 

3 9 

22 

211626 

12-75 

994171 

• 35 

217356 

i 3 -10 

782644 

38 

23 

212291 

12-73 

9941 5 o 

-35 

218142 

i 3 -o 8 

781858 

3 7 

24 

2i3o55 

12-71 

994129 

-35 

218926 

i 3 -o 5 

781074 

36 

25 

21 38 18 

12-68 

994108 

-35 

219710 

i 3 -o 3 

780290 

35 

26 

214279 

12-66 

994087 

•35 

220492 

i 3 -oi 

779508 

34 

27 

2 i 5338 

12-64 

994066 

• 35 

221272 

12-99 

778728 

33 

28 

216097 

12-61 

994045 

•35 

222052 

12.97 

777948 

32 


216854 

12 • 5 9 

994024 

•35 

222830 

12-94 

777170 

3 i 

3 o 

217609 

12-57 

9 94oo3 

•35 

2236 o 6 

12-92 

77 63 9 4 

3 o 

3 i 

9 - 2 i 8363 

12-55 

9-998981 

-35 

9-224382 

12-90 

10-775618 

29 

32 

219116 

12-53 

99 3 9 6 o 

-35 

225 i 56 

12-88 

774844 

28 

33 

219868 

I 2 - 5 o 

99 3 9 3 9 

-35 

228929 

12-86 

774071 

27 

34 

220618 

12-48 

998918 

• 35 

226700 

12 • 84 

7733oo 

26 

35 

221367 

12*46 

99 38 9 6 

•36 

227471 

12 -8i 

772629 

25 

36 

22211 5 

12-44 

993875 

-36 

228239 

12 '19 

771761. 

24 

3 ? 

222861 

12-42 

99 3854 

-36 

229007 

12-77 

770993 

23 

38 

223606 

12 - 3 9 

99 383 2 

-36 

229773 

12-75 

770227 

22 

3 9 

224349 

12-37 

99 38 i1 

-36 

23 o 53 9 

12-73 

769461 

21 

4 o 

226092 

12-35 

993789 

-36 

23 i 3 o 2 

12-71 

768698 

20 

4 i 

9-225833 

12-33 

9-993768 

-36 

9-282065 

12-69 

10-767935 

I 9 

42 

22667 3 

12 • 3 1 

993746 

•36 

282826 

12-67 

767174 

10 

43 

227311 

12-28 

998725 

•36 

233586 

12-65 

766414 

17 

44 

228048 

12-26 

993703 

•36 

234345 

12-62 

765655 

l6 

45 

228784 

12-24 

998681 

-36 

235 1o 3 

12-60 

764897 

i 5 

46 

22 9 5 l 8 

12-22 

993660 

• 36 

235859 

12-58 

764141 

i 4 

47 

230262 

12-20 

998688 

-36 

2366 1 4 

12-56 

763386 

i 3 

48 

23o 9 84 

12- l8 

998616 

-36 

23 7 368 

12-54 

762632 

12 

49 

231714 

12 • l6 

9 9 35 9 4 

* 3 7 

238120 

12-52 

761880 

11 

5 o 

232444 

12 - 14 

993572 

.37 

288872 

I 2 - 5 o 

761128 

10 

5 i 

9-233172 

12-12 

9 -9 9 355o 

• 3 7 

9-239622 

12-48 

10-760378 

9 

52 

233899 

12-0 9 

99 3528 

" 3 7 

240371 

12-46 

769629 

8 

53 

234625 | 

12-07 

9 9 35o6 

* 3 7 

241118 

12-44 

758882 

7 

54 

235349 J 

I 2 -o 5 

993484 

- 3 7 

241865 

12-42 

7681 35 

6 

55 

23607 3 

I 2 -o 3 ' 

993462 

• 3 7 

242610 

12-40 

757390 

5 

56 

286796 

12-01 

993440 

• 3 7 

243354 

12-38 

756646 

4 

3 7 

237615 1 

11-99 

993418 

• 3 7 

244097 

12-36 

755 9 o 3 

3 

5 S 

238235 j 

II -97 

9 9 33 9 6 

* 3 7 

244839 

12-34 

755 i 6 i . 

2 

5 9 

238 9 53 | 

11 - 95 

998374 

• 3 7 

245579 

12-32 

754421 

1 

6 o 

239670 ' 

11 • 9 3 

998861 

• 3 7 

2463 19 

I 2 - 3 o 

7 5368 1 1 

0 

1 


Cosine 

D. 

Sine 


Cotang. 

-2_ 

D. 

Tang, i 

M. j 


(80 DEGREES.) 
















































































28 


(10 DEGREES.) A TABLE OF LOGARITHMIC 


M. | 

Sine 

I). 

Cosine 

D. 

0 

9-239670 

11-93 

o- 99335 i 

.37 

1 

24 o 386 

11 -91 

993329 

-37 

2 

241101 

11-89 

993307 

.37 

3 

241814 

11-87 

993286 

* 3 7 

4 

242626 

n -85 

993262 

• 37 

5 

243237 

u -83 

993240 

- 3 7 

6 

243947 

11 • 8 1 

99 32 1 7 

-38 

7 

244656 

n -79 

993196 

• 38 

8 

245363 

n -77 

99317 2 

• 38 

9 

246069 

ii -75 

993149 

-38 

10 

246770 

ii -73 

998127 

• 38 

11 

9-247478 

11-71 

9-993104 

*38 

12 

248181 

11-69 

993081 

• 38 

i 3 

248883 

11-67 

993059 

•38 

14 

249683 

u -65 

993080 

-38 

i 5 

250282 

n -63 

99301 3 

-38 

16 

250980 

11 • 6 1 

992990 

-38 

*7 

261677 

n-oo 

992967 

• 38 

18 

262373 

11 - Do 

992944 

• 38 

*9 

253067 

n -56 

992921 

*38 

20 

253761 

n -54 

992898 

• 38 

21 

9-254453 

11-52 

9.992870 

*38 

22 

255 i 44 

11 - 5 o 

992S02 

• 38 

23 

255834 

11-48 

992829 

- 3 9 

24 

256523 

11-46 

992806 

• 3 9 

25 

26721 1 

u -44 

992783 

• 3 9 

26 

267898 

11 -42 

992769 

• 3 9 

27 

258583 

11 -41 

992736 

• 3 9 

28 

259268 

11-39 

992713 


29 

269961 

11-37 

992690 

• 39 

3 o 

26o633 

n -35 

992666 

• 3 9 

3 i 

9•261 3 1 4 

n -33 

9-992643 

•39 

32 

261994 

11 • 31 

992619 

'o 9 

33 

262673 

11 - 3 o 

992696 

• 3 9 

34 

26335 i 

11-28 

992072 

• 3 9 

35 

264027 

11-26 

992649 

- 3 9 

36 

264703 

11 • 24 

992020 

•39 

3 7 

266377 

11-22 

992601 

• 3 g 

38 

266o51 

11-20 

992478 

• 40 

39 

266723 

II-I 9 

992404 

,•40 

40 

267395 

11-17 

992430 

•40 

4 1 

9-268065 

11 • 15 

9-992406 

•40 

42 

268734 

11 • 1 3 

992882 

•40 

43 

269402 

11 • 11 

997809 

•40 

44 

270069 

11-10 

992330 

•40 

45 

270735 

11 - 08 

992311 

■40 

46 

271400 

1 1 - 06 

992287 

•40 

47 

272064 

11 - o 5 

992263 

.40 

48 

272726 

11 • o 3 

992239 

•40 

49 

273388 

11 -01 

992214 

•40 

5 o 

274049 

10-99 

992190 

•40 

5 i 

9-274708 

10-98 

9-992166 

I - 4 o 

52 

276367 

10-96 

992142 

•40 

53 

276024 

10-94 

992 17 

• 4 i 

54 

276681 

1 10-92 

992098 

• 4 i 

55 

277337 

10-91 

992069 

• 4 i 

56 

27799 * 

278644 

10-89 

992044 

• 41 

57 

10-87 

992020 

• 4 i 

58 

279297 

io-86 

991996 

| - 4 i 

5 9 

60 

279948 

280099 

j 10*84 
j 10-82 

99 * 97 1 
! 991947 

• 4 i 

• 4 i 


Cosine 

1). 

Sine 



Tang. 

9-246319 

247057 

247794 

24853 o 

249264 

249998 

260780 

201461 

202191 

252920 

253648 

9-264374 

255 ioo 

255824 

266547 

267269 

267990 

258710 

269429 

260146 

260863 

9-261578 
262292 
263 oo 5 
263717 
264428 
2661 38 
260847 
266555 
26)261 
267967 

9-268671 

269375 

270077 

270779 

27*479 

272178 

272876 

273073 

274269 

274964 

9-275668 
276301 
277043 
277734 
278424 
2791i 3 
279801 
280488 
281174 
28 i 858 

9-282642 

283225 

283907 

284088 

286268 

286947 

286624 

287301 

287977 

288652 


D. 


Cotang. 


Cota ng. 


(79 DEGREES.) 


I2-3o 
12-28 
12-26 
12-24 
12-22 
12-20 
12- l8 
12-17 
12-10 

I 2 - 13 
12-11 

I2-09 
12-07 
12-o 5 
12-o3 

I2-OI 

12-00 

11-98 

11-96 

11-94 

II -92 

1 1 -00 
n-8 9 
11-87 
n -85 
u -83 
11 • 81 
11-79 
11-78 
11-76 
ii -74 

11-72 
11-70 
ii- 69 
11 -67 
11 -65 
11-64 
11 -62 
11 - 6o 
u -58 
11-57 

1 1-55 
it -53 
11 • 5 1 
11 - 5 o 
11 -48 
11 -47 
ii-45 
ii-43 

11 -41 

u- 4 o 

u -38 
11 -36 
ii *35 
u -33 
11 • 3 1 
11 - 3 o 
11-28 
11-26 
11 • 26 
11-23 


10-753681 
752943 
752206 
701470 
760736 
760002 
749270 
748539 
747809 
747080 
746352 

10-745626 
744900 
744176 
743453 
742731 
742010 
741290 
740671 
739854 
739137 

10-738422 

7 3 77 o 8 

736995 
736283 
735572 
734862 
734 i 53 

733445 
732739 
732 o 33 

10-731329 
730625 
729923 
729221 
728621 
727822 
727124 
726427 
726731 
725 o 36 

10*724342 

723649 

722967 
722266 
721676 
720880 
720199 
719612 
718826 
718142 

10-717468 
716775 
716093 
716412 ' 

714732 

714063 j 
713376 | 
712699 : 
712023 i 
711348 


! 60 I 
! 5 o i 
! 58 I 
i 67 ! 

56 I 
1 55 ! 
i 54 : 
! 53 I 
i 52 ; 

1 5 1 I 

I 60 1 

i 4 < 

i 4 ' 

| 47 
46 
45 
. 44 
1 43 
1 42 
4 i 
40 

3 9 
38 
I 37 
36 
, 35 

! 34 

} 33 

32 

: 3 i 
3 o 

29 
28 
27 
26 
25 

24 

! 23 

22 

20 


1 

I 

17 

16 

i 5 

14 

i3 

12 

II 
10 


7 

6 

5 

4 

3 

2 

1 

o 


D. 


T ang. 1 M. 















































































SINES AND TANGENTS. (11 DEGREES.) 


29 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-280599 

10-82 

9.991947 

• 4 i 

9-288652 

11-23 

10-711348 

60 

i 

281248 

10 • 81 

991922 

• 4 i 

289326 

11-22 

710674 

5 9 

58 

3 

281897 

io -79 

991897 

• 4 i 

289999 

11-20 

710001 

3 

282544 

10-77 

991873 

•41 

290671 

11 - l8 

709329 

708658 

67 

4 

283190 

10-76 

991848 

• 41 

291342 

11-17 

56 

5 

283836 

10-74 

991823 

• 41 

292013 

11 • 15 

707987 

55 

6 

284480 

10-72 

991799 

•41 

292682 

11 • 14 

707318 

54 

7 

285124 

10-71 

, 991774 

•42 

293350 

II -12 

706660 

53 

8 

980766 

10-69 

991749 

•42 

294017 

11 • II 

706983 

52 

9 

286408 

10-67 

991724 

.42 

294684 

11-09 

7 o 53 i 6 

5 i 

10 

287048, 

io-66 

991699 

•42 

295349 

11-07 

704681 

5 o 

1 1 

9-287687 

10-64 

9-991674 

•42 

9-296013 

11 - 06 

10-703987 

49 

1 2 

288326 

io -63 

991649 

• 42 

296677 

1 1 • 04 

7 o 3323 

4 i 3 

i 3 

288964 

io-6i 

991624 

• 42 

297339 

11 - o 3 

702661 

47 

14 

289600 

10-59 

991599 

•42 

298001 

II -01 

701999 

46 

i 5 

290236 

io -58 

991574 

•42 

298662 

11 • 00 

70 i 338 

45 

16 

290870 

io -56 

99 i 549 

•42 

299322 

10-98 

700678 

44 

17 

291604 

io -54 

991624 

•42 

299980 

10-96 

700020 

43 

18 

292137 

io -53 

991498 

•42 

3 oo 638 

10-96 

699362 

42 

i 9 

292768 

io- 5 i 

99147-8 

•42 

301296 

10-93 

698706 

4 i 

20 

293399 

io- 5 o 

991448 

•42 

301901 

10-92 

698049 

4 o 

21 

9-294029 

10-48 

9-991422 

•42 

9-302607 

10-90 

10-697893 

3 Q 

22 

294658 

10-46 

991397 

• 42 

3 o 326 i 

10-89 

696739 

38 

23 

296286 

10-45 

991372 

•43 

303914 

10-87 

696086 

87 

24 

295913 

10-43 

991346 

•43 

304367 

io-86 

696433 

36 

25 

296539 

10-42 

991321 

•43 

3 o 32 i 8 

10-84 

694782 

35 

26 

297164 

10-40 

991295 

•43 

3 o 5869 

io -83 

6941 3 1 

34 

27 

297788 

10-39 

991270 

-43 

306019 

io-8i 

693481 

33 

28 

298412 

10-37 

991244 

•43 

307168 

io-8o 

692882 

32 

29 

299084 

io -36 

991218 

•43 

307816 

10-78 

692185 

3 i 

3° 

299655 

io -34 

991193 

•43 

3 o 8463 

10-77 

691537 

3 o 

! 3 i 

9-300276 

10-32 

9 • 9*91167 

•43 

9-309109 

10-75 

10-690891 

29 

32 

300890 

io- 3 i 

99U41 

•43 

309754 

10-74 

690246 

28 

33 

3 oi 5 i 4 

10-20 

99111 5 

•43 

3 io 3 9 S 

10-73 

689602 

27 

34 

302132 

10-28 

991090 

•43 

3 11042 

10-71 

688 g 58 

26 

35 

302748 

10-26 

991064 

•43 

3 i1 685 

10-70 

6883 1 5 

25 

36 

3 o 3364 

10- 25 

9910.88 

•43 

312327 

io-68 

687673 

24 

3 ? 

303979 

10-23 

991012 

•43 

3 12967 

10-67 

6870.33 

23 

38 

30409.3 

10- 22 

990986 

•43 

3 i 36 o 8 

io -65 

686392 

22 

3 g 

3 o 52 o 7 

10-20 

990960 

•43 

314247 

10-64 

680703 

21 

40 

3 o 58 i 9 

I 0 -I 9 

990934 

•44 

3 1 4885 

10-62 

685 1i 5 

20 

4 1 

42 

9- 3 o 643 0 

307041 

10-17 

10- 16 

9-990908 

990082 

•44 

•44 

9- 3 1 5523 

3 16159 

io-6i 
io-60 

10-684477 

683841 

■13 

43 

307660 

10- 14 

990855 

•44 

316790 

io -53 

683205 

17 

44 

308209 

10- l 3 

990829 

•44 

3 17430 

io -57 

682670 

16 

45 

308867 

10- I I 

990803 

•44 

3 18064 

io -55 

681986 

i 5 

46 

309474 

10- 10 

990777 

•44 

3 18697 

io -54 

68 i 3 o 3 

14 

47 

3 ioo 8 o 

10-08 

990760 

•44 

819329 

io -53 

680671 

i 3 

48 

3 io 685 

10-07 

990724 

•44 

319961 

io- 5 i 

680089 

679.408 

12 

49 

3 11289 

10 • o 5 

990697 

•44 

320092 

10- 5 o 

11 

5 o 

311898 

10-04 

990671 

•44 

321222 

10-48 

678778 

10 

j 5l 

9 - 3 12496 

10 • o 3 

9-990644 

•44 

9 * 32185 1 

10-47 

10-678149 

0 

52 

3 13097 

IO-OI 

990618 

•44 

322479 

io -45 

677521 

8 

53 

3 13698 

10-00 

990691 

•44 

323 too 

io -44 

676894 

7 

54 

314297 

9-98 

990565 

•44 

323733 

io -43 

676267 

6 

55 

3 7 4897 

9 '97 

990538 

•44 

324358 

10-41 

670642 

5 

56 

310496 

9-96 

990511 

•43 

3249-83 

10-40 

676017 

4 

27 

316092 

9.94 

990480 

•40 

320607 

10-39 

67439.3 

3 

58 

316689 

9-98 

990408 

•43 

326281 

10-37 

678769 

2 

59 

317284 

69, 

990431 


326853 

io -36 

67.8147 

1 

60 

' 317879 

9.90 

9904 '4 

•45 

327475 

io -35 

672026 

0 

L I 

Cosine 

D. 

Sine 


Cotang. 

D. 

Tang. 

M. 


(78 DECREES.) 


y 
































































30 (12 DEGREES.) A TABLE OF LOGARITHMIC 


r 

M. 

Sine 

D. 

Cosine 

D, 

Tang. 

D. 

Cotang. 


o 

9.317879 

9-90 

9.990404 

• 45 

9.327474 

io-35 

10-672626 

60 

i 

3 i 84?3 

9-88 

990378 

•45 

328096 

io-33 

671906 

5q 

2 

319066 

9.87 

990361 

•45 

328715 

10-32 

671285 

58 

3 

3io658 

9-86 

990324 

•45 

329634 

io-3o 

670666 

57 

4 

320249 

9-84 

990297 

•45 

329968 

10-29 

670047 

56 

5 

320840 

9-83 

990270 

•45 

33057ft 

10-28 

669430 

55 

6 

32i43o 

9-82 

990243 

.45 

331187 

10-26 

668813 

o4 

7 

322019 

9-80 

990215 

•45 

33i8o3 

10-25 

668197 

53 

8 

322607 

9-79 

990188 

•45 

332418 

10-24 

667682 

52 

! 9 

320194 

9-77 

990161 

• 45 

333o33 

10-23 

666967 

5i 

1 u 

823780 

Q • 76 

990134 

•45 

333646 

10-21 

666354 

5o 

i \ 

9-324366 

9.75 

9.990107 

.46 

9.334259 

10-20 

io- 66574 i 

49 

12 

324 q 5 o 

9-73 

990079 

.46 

334871 

10-19 

666129 

48 

i3 

325534 

9-72 

990052 

•46 

335482 

10-17 

664618 

47 

U 

326117 

9-70 

990025 

•46 

336093 

10- 16 

663907 

46 

i5 

326700 

9.69 

989997 

•46 

336702 

io-15 

663298 

4"5 

i6 

327281 

9.68 

989970 

.46 

337611 

io-13 

662689 

44 

17 

327862 

9-66 

989942 

.46 

3879 19 

10-12 

662081 

43 

i8 

328442 

9*65 

989915 

.46 

338527 

IO- I I 

661473 

42 

19 

329021 

9-64 

989887 

•46 

33 9 i 33 

IO- IO 

660867 

4i 

20 

329599 

9-62 

989860 

•46 

339739 

io-o8 

660261 

4o 

21 

9.330176 

9-61 

9.989832 

.46 

9•34o344 

10-07 

10-659656 

3 9 

22 

330753 

9.60 

989804 

.46 

340948 

io-o6 

659052 

38 

23 

331329 

9-58 

989777 

•46 

34 i 552 

io-o4 

658448 

37 

24 

33190! 

9.57 

989749 

'47 

342i55 

io-o3 

657845 

36 

25 

332478 

9-56 

989721 

•47 

342757 

10-02 

657243 

35 

26 

333o5i 

9-54 

989698 

•47 

343358 

10-00 

656642 

34 

27 

333624 

9-53 

989665. 

•47 

343958 

9.99 

666042 

33 

28 

334195 

9-52 

989687 

•47 

344558 

9.98 

655442 

32 

29 

334766 

9-5 o 

989609 

•47 

346167 

9’97 

654843 

3i 

3o 

335337 

9.49 

989682 

•47 

345756 

9.96 

654245 

3o 

3i 

9.335906 

9.48 

9.989553 

•47 

9.346353 

9-94 

10-653647 

2^ 

32 

336475 

9.46 

98962s 

•47 

346949 

9-93 

653o5i 

28 

33 

337043 

9-45 

989497 

•47 

347545 

9-92 

652455 

27 

34 

337610 

9-44 

989469 

•47 

348141 

9-9 1 

651869 

26 

35 

338176 

9-43 

989441 

•47 

348735 

9.90 

65i265 

25 

36 

338742 

9.41 

989413 

•47 

349629 

9-88 

660671 

24 

' 37 

339306 

9-40 

989384 

•47 

349922 

9-87 

660078 

23 

38 

339871 

9.39 

989866 

•47 

35 o 5 i 4 

9-86 

649486 

22 

3 9 

340434 

9.37 

989828 

•47 

351106 

9-86 

648894 

21 

40 

340996 

9-36 

989300 

•47 

351697 

9-83 

6483o3 

20 

4i 

9-34 i 558 

9-35 

9-989271 

•47 

9.352287 

9-82 

10-647713 

IO 

42 

342119 

9.34 

989243 

•47 

352876 

9-81 

647124 

IO 

43 

342679 

9-32 

989214 

•47 

353465 

9-80 

646535 

IT 

44 

343239 

9 • 31 

989186 

•47 

354o53 

9-79 

645947 

16 

45 

343797 

9*3 o 

989157 

•47 

354640 

9-77 

64536o 

i5 

46 

344355 

9-29 

989128 

.48 

35.6227 

9-76 

644773 

14 

47 

344912 

9.27 

989100 

.48 

3558 i 6 

9-75 

644187 

i3 

48 

346469 

9-26 

989071 

.48 

3563g8 

9-74 

643602 

12 

49 

346024 

9-25 

989042 

•48 

356982 

9-73 

643018 

11 

5o 

346579 

9-24 

989014 

• 48 

357066 

9.71 

642434 

10 

5i 

9-347i34 

9-22 

9-988985 

• 48 

9.358149 

9.70 

io- 64 i 85 i 

Q 

52 

347687 

9.21 

988966 

.48 

35873 i 

9.69 

641269 

8 

53 

348240 

9*20 

988927 

• 48 

35g6i3 

9-68 

640687 

7 

54 

848792 

9-!9 

988898 

• 48 

359898 

9.67 

640107 

6 

55 

349848 

9-n 

988869 

• 48 

360474 

9-66 

639526 

5 

56 

349893 

9.16 

988840 

• 48 

36io53 

9-66 

638947 

4 

57 

35 o 443 

9 • 15 

988811 

•49 

36 i 632 

9-63 

638368 

3 

58 

350992 

9-14 

988782 

•49 

362210 

9-62 

687790 

1 2 

59 

35 i 54 o 

9. i3 

988753 

•49 

362787 

9-61 

637213 

1 

60 

352 o 88 

9.11 

988724 

•49 

; 363364 

9-60 

| 636636 

I 0 


Cosine 

D. 

Sine 

Cotang. 

D. 

! Tang. 

M. | 


(77 DEGREES.) 



































































SINES AND TANGENTS. (13 DEGREES.) 


81 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

1 

2 

3 

4 

5 

* 6 

7 

8 

9 

IO 

1 ii 

1 12 

13 

14 

15 

16 

*7 

18 

1 9 

20 

2 I 
22 

23 

24 

25 

26 

27 

28 

J2 

31 

32 

33 

34 

35 

36 

87 

38 

3 9 

40 

41 

42 

43 

44 

45 

46 

47 

48 

to 

51 

52 

53 

54 

55 

54 

ll 

tl 

g-352o88 
352635 
353181 
353726 
354271 
3548 i 5 
355358 
355901 
356443 

356984 

357624 

9-358 o 64 

3586o3 

359141 

359678 

36o2i5 

360752 

361287 

361822 

362356 

362889 

9*363422 

363g54 

364485 

365oi6 

355546 

866075 

3666o4 

367131 

367669 

368i85 

9-368711 

36g236 

369761 

370285 

370808 

37i33o 

371852 

372373 

372894 

373414 

9-373933 

374452 

374970 

375487 

376006 

376519 

377035 

377549 

378063 

878577 

9-379089 
379601 
38 oii 3 
380624 
38ii34 
38 i 643 
382152 
382661 
383168 
383675 

9*n 

9-10 

9-°q 

9-08 

9-07 

g-o5 

9-04 

9-o3 

9-02 

9-01 

8-99 

8-98 

8-97 

8-96 

8- 9 5 

8- 9 3 

8-92 

8-91 

8-90 

8-89 

8-88* 

8-87 

8-85 

8-84 

8-83 

8-82 

8 • 81 

8-80 
8-79 
8-77 
8-76 

8-75 

8-74 

8 • 73 

8-72 

8-71 

8-70 

8-69 

8-67 

8-66 

8-65 

8-64 

8-63 

8-62 

8 • 61 

8-60 
8-5 9 
8-58 
8-5 7 
8-56 
8-54 

8-53 

8-52 

8 • 51 
8-5o 

8-49 

8-48 

8-47 

8-46 

8-45 

8-44 

9-988724 

988695 

988666 

988636 

988607 

988578 

988548 

988519 

988489 

- 988460 
988430 

9-988401 
9 883 7 i 
988342 
9 88312 
988282 
988262 
988223 
988193 
988163 
9 88 i 33 

9-988103 

988073 

988043 

988013 

987983 

987953 

987922 

987S92 

987862 

987832 

9-987801 

987771 

987740 

987710 

987679 

987649 

987618 

987588 

987557 

987526 

9-987496 

987465 

987434 

987403 

987372 

987341 

987310 

987279 

987248 

987217 

9-987186 
' 9 8 7 i 55 
987124 
987092 
987061 
987030 
986998 
986967 
986936 
986904 

.49 

•49 

•49 

.49 

.49 

•49 

.49 

.49 

.49 

• 49 

• 49 

• 49 
.49 

:fo 

•5o 

•5o 

• 5o 

• 5o 

• 5o 

• 5o 

•5o 

•5o 

• 5o 
-5o 
-5o 

• 5o 

• 5o 

• 5o 

• 5o 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 5i 

• 62 
•52 
•52 
•52 
•52 
•52 
•52 

•52 
•52 1 
•52 

• 62 

• 62 

• 62 
•52 
•52 
•52 

• 62 

9-363364 
363940 
364515 
365090 
365664 
366237 
3668io 
367382 
367953 
368524 
369094 

9-369663 

370232 

370799 

371667 

371936 

372499 

373064 

373629 

374193 

374756 

9-375319 

3 7 588i 

376442 

377003 

377563 

378122 

378681 

379289 

379797 

38o354 

9-380910 

38U66 

382020 

382675 

383i29 

383682 

384234 

384786 

385337 

385888 

9-386438 

386987 

387536 

388o84 

38863i 

389178 

389724 

390270 

390815 

391360 

9-391903 

392447 

393531 

394073 

3946l4 

395l54 

395694 

396233 

39677I 

1 

9-60 

9-69 

9-58 

9-5? 

9-55 

9-54 

9-53 

9-62 

9-5 i 

9-5 o 

9-49 

9-48 

9-46 

9-45 

9-44 

9-43 

9-42 

9-41 

9-40 

9-3 9 

9-38 

9-37 

9-35 

9-34 

9-33 

9-32 

9 • 31 
9-3 o 
9-29 
9-28 
9-27 

9-26 

9-25 

9-24 

9-23 

9-22 

9-21 

9-20 

9.no 

9-18 
9-17 

9 • 15 
9 -i 4 

9-13 
9-12 
9-n 
9-10 
9-09 
9-08 
9-07 
9-06 

9 -o 5 

9-04 

9 -o 3 

9-02 

9-01 

9-00 

8# 

8. 97 

8-96 

10-636636 

636o6o 

635485 

634910 

634336 

633763 

633190 

632618 

632047 

631476 

630906 

io- 63 o 337 

629768 

629201 

628633 

628067 

627501 

626986 

626371 

626807 

625244 

10-624681 
624119 
623558 
622997 
622437 
621878 
621319 
620761 
620203 
619646 

10-619090 

6 i 8534 

617980 

617425 
616871 
616318 
616766 
6 i 52 i 4 
614663 
614112 

io- 6 i 3562 

6 i 3 oi 3 

612464 

611916 

611869 

610822 

610276 

609730 

609186 

608640 

10-608097 

607553 

607011 
606469 
605927 
6o5386 
604846 
6o43o6 
603767 
603229 

60 

59 

58 

57 

56 

55 

54 

53 

52 

5i 

5o 

49 

48 

47 

46 

45 

44 

43 

42 

4i 

40 

3 9 

38 

37 

36 

35 

34 

33 

32 

3i 

3o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

l8 

17 

l6 

i5 

14 

i3 

12 

11 

10 

7 

6 

5 

4 

3 

2 

1 

0 

Cosine 

D. 

Sine 1 


Cotang. 

D. 

Tang. 

M. 


26 


(76 DEGREES.) 
























































32 


(14 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

-- 

0 

9• 3836 7 5 

8-44 

9•986904 

•52 

9-396771 

8-96 

10-603229 

60 

i 

384182 

8-43 

986873 

-53 

397309 

8.96 

602691 

69 

2 

384687 

8-42 

986841 

-53 

3 97846 

8-90 

602104 

58 

3 

386192 

8- 41 

986809 

-53 

398383 

8-94 

601617 

37 

4 

385697 

8-40 

986778 

-53 

398919 

8 • 93 

601081 

56 

5 

386201 

8 - 3 9 

986746 

• 53 

399455 

8-92 

600645 

55 

6 

386704 

8-38 

986714 

• 53 

399990 

8-91 

600010 

54 

7 

387207 

8-37 

986683 

• 53 

4 oo 524 

8-90 

699476 

53 

8 

387709 

8-36 

986601 

-53 

4 oio 58 

8-89 

598942 

52 

o 

388210 

8-35 

986619 

• 53 

401591 

8 • 88 

598409 

5 i 

10 

388711 

8-34 

986587 

• 53 

402124 

8-87 

597876 

5 o 

11 

9-389211 

8-33 

g -986555 

-53 

9-402656 

8-86 

10-697344 

49 

12 

389711 

8-32 

986528 

• 53 

403187 

8-85 

596813 

48 

i 3 

390210 

8 - 3 1 

986491 

-53 

403718 

8-84 

596282 

47 

14 

390708 

8 - 3 o 

986409 

-53 

404249 

8-83 

5 g 5 -] 5 i 

46 

i 5 

391206 

8-28 

986427 

-53 

404778 

8-82 

596222 

45 

16 

391703 

8-27 

986395 

• 53 

4 o 53 o 8 

8 • 81 

594692 

44 

17 

392199 

8-26 

986363 

•54 

4 o 5836 

8- 80 

694164 

43 

18 

392696 

8-25 

986331 

• 54 

4 o 6364 

8-70 

59-3636 

42 

19 

393191 

8-24 

986299 

.54 

406892 

8-78 

5 g 3 108 

4 i 

20 

393685 

8-23 

986266 

•54 

407419 

8-77 

592581 

40 

21 

9-394179 

8-22 

9-986234 

.54 

9-407945 

8-76 

io- 592 o 55 

3 9 

22 

394678 

8-21 

986202 

.54 

408471 

8-75 

591529 

38 

23 

390166 

8-20 

986169 

.54 

408997 

8-74 

591003 

37 

24 

3 9 5658 

8-19 

986137 

.54 

409021 

8-74 

590479 

36 

25 

396160 

8-i8 

986104 

•54 

410045 

8-73 

589955 

35 

26 

396641 

8-17 

9S6072 

.54 

410569 

8-72 

589431 

34 

27 

397132 

8-17 

986039 

.54 

411092 

8-71 

58S908 

33 

28 

397621 

8-16 

986007 

.54 

41161 5 

8-70 

5883 S 5 

32 

29 

3 q 8 i r1 

8 • 1 5 

985974 

.54 

412137 

8-60 

58 7 863 

3 i 

3 o 

398600 

8-14 

985942 

•54 

412658 

8-68 

587342 

3 o 

3 i 

9•399088 

8 -1 3 

9-985909 

• 55 

9-413179 

8-67 

io- 58682 i 

29 

32 

3 gg 5 j 5 

8-12 

985876 

• 55 

413699 

8-66 

5863 01 

28 

33 

400062 

8-u 

985843 

• 55 

414219 

8-65 

686781 

27 

34 

400649 

8-10 

985811 

• 55 

414738 

8-64 

535262 

26 

35 

4 oio 3 o 

8-09 

98577S 

• 55 

416267 

8-64 

584743 

25 

36 

401020 

8-08 

985746 

• 55 

416770 

8-63 

584225 

24 

37 

402006 

8-07 

985712 

• 55 

416293 

8-62 

583707 

23 

38 

402489 

8-06 

985679 

• 55 

416810 

8 • 61 

583190 

22 

39 

402972 

8 -o 5 

986646 

• 55 

417326 

8-60 

582674 

21 

40 

403455 

8-04 

9856 i 3 

• 55 

417842 

8-59 

582 i 58 

20 

4 i 

9-403938 

8 -o 3 

9-985580 

• 55 

9 - 4 i 8358 

8-58 

io- 58 i 642 

IO 

42 

404420 

8-02 

985547 

• 55 

418873 

8-57 

58 1127 

10 

43 

404901 

8-oi 

9855 i 4 

• 55 

419387 

8-56 

58 o 6 i 3 

17 

44 

4o5382 

8-00 

985480 

• 55 

419901 

8-55 

580099 

l6 

45 

406862 

7-99 

980447 

• 55 

42 o 4 i 5 

8-55 

579685 

i 5 

46 

4 o 634 i 

7-98 

985414 

• 56 

420927 

8-54 

579073 

i 4 

47 

406820 

7-97 

98538 o 

• 56 

42144o 

8-53 

57&60 

i 3 

48 

407299 

7-96 

985347 

• 56 

421952 

8-52 

578048 

12 

49 

407777 

7-96 

9853 i 4 

-56 

422463 

8 • 5 1 

577537 

11 

5 o 

408254 

7-94 

985280 

• 56 

422974 

8 - 5 o 

677026 

10 

5 i 

9-408731 

7-94 

9-985247 

• 56 

9-423484 

8-49 

io- 5765 i 6 

Q 

52 

409207 

7 - 9 3 

985213 

• 56 

423(793 

8-48 

576007 

8 

53 

409682 

| 7 - 9 2 

980180 

• 56 

424003 

8-48 

676407 

7 

54 

410167 

7.91 

985146 

• 56 

426011 

8-47 

574989 

6 

55 

4 io 632 

7-00 

9851i 3 

-56 

426519 

8-46 

574481 

5 

56 

411106 

7-89 

986079 

• 56 

426027 

8-45 

573973 

4 

57 

411579 

7-88 

986040 

• 56 

426534 

8-44 

573466 

3 

58 

412002 

7-80 

980011 

• 56 

1 427041 

8-43 

572969 

2 

59 

412624 

7-86 

984978 

• 56 

427547 

8-43 

572453 

1 

60 

412996 

7-85 

984944 

• 56 

1 428062 

1 

8-42 

571948 

° 


Cosine 

D. 

Sine 


! Cotang. 

1 D- 

Tang. 

M. 


(75 DEGREES.) 




































































SINES AND TANGENTS. (15 DEGREES.) 33 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

1 

2 

3 

4 

5 

6 

9 

10 

11 

12 

»3 

14 

10 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

41 

42 

43 

44 
46 

46 

47 

48 

49 

5 0 

5 1 
; 62 
* 53 

54 

55 

56 

5 7 
53 

59 

60 

9-412996 

413467 

413938 

414408 

414878 

4 i 5347 

4 i 58 i 5 

416283 

416761 

417217 

417684 

9 - 4 i 8 i 5 o 

41861 5 
419079 

419644 

420007 

420470 

420933 

421395 

421867 

4223 i 8 

9-422778 
423238 
423697 
424106 

4246 i 5 

425073 

42553o 

425987 

426443 

426899 

9-427354 

427809 

428263 

428717 

429170 

429628 

430076 

43 o 527 

430978 

431429 

9-431879 

432329 

432778 

433226 

433675 

434122 

434669 

435 oi 6 

435462 

435908 

J d -436353 
, 436798, 

437242 

1 437686 

488129 
438572 
4390 1 4 
439406 
439897 

44 o 338 

7-85 

7*84 

7-83 

7-83 

7-82 

7-81 

7-80 

7 - 7 ? 

7.78 

I'll 

7-76 

7-70 

7-74 

7-73 

7-73 

7-72 

7-71 

l-io 

7‘ 6 9 

7-68 

7-67 

7-67 

7-66 

7-65 

7-64 

7-63 

7-62 

7 * 6 i 

7-60 

7-60 

7 - 5 9 

7*53 

7-07 

7-56 

7 - 55 
7-54 
7-53 
7-52 
7-52 
7 - 5 i 
7 - 5 o 

7-49 

7-49 

7.48 

7-47 

7-46 

7-40 

7-44 

7-44 

7-43 

7-42 

7 - 4 i 
7-40 
| 7-40 

7-39 

7-38 

7-37 

7-36 

7-36 

7-35 

7-34 

9-984944 

984910 

984876 

984842 

984808 

984774 

984740 

984706 

984672 

984637 ; 

984603 

9-984569 1 
984035 
984600 
984466 
98448 2 
984397 
984363 
984328 
984294 
984269 

9-984224 

984190 

984105 

984120 

984085 

984060 

984016 

983981 

983946 

983911 

9-988875 

983840 

9 838 o 5 

983770 

933735 

983700 

9 83664 

983629 

983594 

983558 

9-983623 

983487 

983452 
983416 
9 8338 1 
983345 
983309 
983278 
9 83238 
| 983202 

9 - 9 83 i 66 

9 83 i 3 o 

1 983094 

! 983 o 08 

983022 
9829S6 
982950 
982914 
982878 
982842 

.57 

•57 

.07 

•57 

•37 

•57 

•57 

•57 

I 7 

- 5 ? 

•57 

- 5 7 

• 5 7 

•37 

• 67 

• 58 
-58 
-58 
-58 

• 58 
-58 

-58 

-58 

-58 

• 58 
-58 
-58 
-58 
-58 
-58 
-58 

• 58 

i 9 

• 69 
- 5 9 

I 9 

- 5 9 

I 9 

| 

- 5 9 

•39 

•39 

• 5 9 
- 5 9 

| 

• o 9 

| -6o 
! ■ 60 
j -6o 

■ 60 
i -6o 

• 60 

■ 60 

• 60 

• 60 

• 60 

• 60 
60 

• 60 

9 -428o52 
42855 7 
429062 
42 9 566 1 
430070 
480573 
431070 
431677 
432079 
43258 o 
433 o 8 o 

9- 43358 o 
434080 
434679 
430078 
435576 
436073 

436570 
437067 
43 1 563 
438 o 0 9 

9*438554 

439048 

439043 

44 oo 36 
440629 
441022 
44 i 5 14 
442606 

442497 

442988 

9-443479 

443968 

444458 

444947 

445435 

445923 

446411 

446898 

447384 

447870 

9*448356 

448841 

44 9 326 

44 9 8io 

460294 

450777 

461260 

461743 

452225 

452706 

9-453187 

453668 

454148 

454628 

466107 

455586 

466064 

456542 

457019 

407496 

8-42 

8-41 

8* 40 
8-39 
8-38 
8-38 
8-37 
8-36 
8-35 
8-34 
8-33 

8-32 

8-32 

8 • 3 1 
8 * 3 o 
8-29 
8-28 
8-28 
8-27 
8-26 
8-25 

8-24 

8-23 

8-23 

8-22 

8-21 

8-20 

8-19 
8-19 
8-18 
8-17 

8-16 

8-16 

8* i 5 

8-14 

8 • 1 3 
8-12 
8-12 

8-11 
8-io 
8-09 

8-09 

8-o8 

8-07 

8-06 

8-06 
8 -o 5 
8-04 
8 -o 3 
8-02 
8-02 

8-oi 

8-oo 

1-99 

7.99 

7-98 

1-91 

7.90 

7-96 

7-90 

7-94 

10-571948 
571443 
570938 
670434 
56 99 3 o 
569427 
568926 
568423 
667921 1 
667420 
566920 

10-666420 

566920 

565421 

664922 

664424 

563 9 27 

56343 o 

662933 

562437 

561941 

io- 56 i 446 

560962 

660467 

669964 

559471 

508978 

558486 

557994 

5575 o 3 

557012 

10-556521 
556 o 32 
555542 
555 o 53 
554565 
554077 
553589 
553 102 
5526 i 6 
552 i 3 o 

io- 55 i 644 
55 1169 

550674 

550190 

549706 

549223 

548740 

548267 

54777 s 

547294 

10•54681 3 
546332 
545852 
545372 
544898 
544414 
543 9 36 
543458 

542981 

542604 

60 

5 q 

58 

57 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 

42 

4 i 

4 o 

39 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

I 9 

10 

17 

l6 

i 5 

i 4 

i 3 

12 

11 

10 

7 

6 

5 

4 

3 

2 

1 

0 

1 

l 

< 

Cosine 

1 D. 

1 Sine 


Cotang. I D. 

O -—-- 

Tang. 

M. 


(74 DEGREES.) 

































































34 (16 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

L>. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

• 44 o 338 

7-34 

9-982842 

• 60 

9-457496 

7-94 

io- 5425 o 4 

60 

i 

440778 

7-33 

982805 

• 60 

457973 

?- 9 3 

542027 

& 

2 

441218 

7-32 

982769 

•61 

458449 

7 - 9 3 

54 i 55 i 

58 

3 

441 658 

7 • 3 1 

982733 

• 61 

458920 

7.92 

641076 

07 

4 

442096 

7 * 3 1 

982696 

• 61 

459400 

7.91 

540600 

06 

5 

442535 

7 - 3 o 

982660 

•6i 

469875 

7.90 

540125 

55 

6 

442973 

7-29 

982624 

•61 

460349 

7 - 9 ° 

589661 

54 


443410 

7-28 

982687 

•61 

460823 

7‘«9 

039177 

53 

6 

443847 

7-27 

982551 

•61 

461297 

7-88 

538703 

52 

o 

444284 

7-27 

982514 

•6i 

461770 

7 • 88 

53823o 

5 i 

10 

444720 

7-26 

982477 

•61 

462242 

7-87 

537708 

5 o 

11 

9 - 445 i 55 

1-20 

9-982441 

•61 

9-462714 

7*86 

10-537286 

49 

12 

445590 

7-24 

982404 

•61 

463 186 

7-85 

5368 i 4 

48 

i 3 

446025 

7-23 

982367 

•61 

463658 

7-85 

536342 

47 

U 

446409 

7 • 23 

982331 

•61 

464129 

7-84 

535871 

46 

i 5 

446893 

7-22 

982294 

•61 

464699 

7*83 

535401 

45 

16 

447326 

7-21 

982237 

•61 

466069 

7 -83 

534931 

44 

17 

447759 

7-20 

982220 

•62 

460539 

7-82 

53446 i 

43 

18 

448191 

7-20 

982183 

•62 

466008 

7-81 

033992 

42 

19 

448623 

7-19 

982146 

•62 

466476 

7-80 

033024 

4 i 

20 

449034 

7.18 

982109 

•62 

466945 

7-80 

533 o 5 o 

4 o 

21 

9-449485 

7 -n 

9-982072 

•62 

9-467413 

7*79 

10 - 53258 / 


22 

4499 i 5 

7-16 

982035 

•62 

467880 

7-78 

532120 

38 

23 

45 o 345 

7-16 

981998 

•62 

468347 

7.78 

53 1 653 

3 7 

24 

430775 

7 • 1 5 

981961 

•62 

468814 

7*77 

53 1186 

36 

25 

45 1204 

7*14 

981924 

•62 

469280 

7-76 

530720 

35 

26 

43 i 632 

7 • 1 3 

981886 

•62 

469746 

7.70 

53 o 254 

34 

27 

432060 

7 -i 3 

981849 

•62 

470211 

7.75 

529789 

33 

28 

432488 

7-12 

981812 

•62 

470676 

7-74 

52 q 324 

32 

29 

4320 1 5 

7*11 

981774 

•62 

471i4i 

7 - 7 3 

028809 

3 i 

3 o 

453342 

7-10 

981737 

•62 

471605 

7 - 7 3 

528390 

3 o 

3 i 

9-453768 

7-10 

9-981699 

•63 

9-472068 

7.72 

10-527932 

29 

32 

454194 

7-09 

981662 

•63 

472532 

7.71 

527468 

2b 

33 

454619 

7-08 

981625 

•63 

472995 

l‘li 

527005 

27 

34 

455 o 44 

7-07 

981387 

•63 

473407 

7.70 

526543 

26 

35 

455469 

7-07 

981649 

•63 

473919 

7-69 

526081 

25 

36 

4558 9 3 

7-06 

981512 

•63 

47438 i 

7-69 

026619 

24 

37 

4563 16 

7 -o 5 

981474 

•63 

474842 

7-68 

520158 

23 

38 

456739 

7-04 

981436 

•63 

4753 o 3 

7.67 

524697 

22 

39 

437162 

7-04 

981399 

•63 

475763 

7-67 

524237 

21 

40 

457084 

7 -o 3 

981361 

•63 

476223 

7-66 

523777 

20 

41 

9 - 458 oo 6 

7-02 

9-981323 

•63 

9*476683 

7-65 

io- 5233 i 7 

.19 

42 

468427 

7-01 

981285 

•63 

477142 

7-65 

522858 

18 

43 

458848 

7-01 

981247 

•63 

477601 

7-64 

522399 

H 

44 

439268 

7-00 

981209 

•63 

478059 

7-63 

521941 

l6 

45 

459688 

6-99 

981171 

•63 

478617 

7-63 

521483 

i 5 

46 

460108 

6-98 

98 n 33 

• 64 

478970 

7-62 

521025 

14 

47 

460327 

6-98 

981095 

•64 

479432 

7-61 

520568 

i 3 

48 

460946 

6-97 

981067 

• 64 

479889 

7-61 

5201 11 

12 

49 

461364 

6-96 

981019 

•64 

480340 

7-60 

519605 

11 

5 o 

461782 

6- 9 5 

980981 

•64 

480801 

7-59 

519199 

10 

5 i 

9-462199 

6-95 

9-980942 

• 64 

9-481257 

7 - 5 o 

10-518743 

0 

5 a 

462616 

6-94 

980904 

• 64 

481712 

7-58 

518288 

8 

53 

463 o 32 

6-93 

980866 

• 64 

482167 

7-57 

5 1 7 833 

7 

54 

463448 

6-93 

980827 

• 64 

482621 

7-5 7 

5 i 7 3 79 

6 

55 

463864 

6-92 

980789 

•64 

483076 

7-56 

616926 

5 

56 

464279 

6-91 

980760 

• 64 

483529 

7 • 55 

516471 

4 

57 

464694 

. 6-90 

980212 

• 64 

483982 

7-55 

5 i 6 oi 8 

3 

58 

465 108 

6 -oo 

980673 

.64 

484435 

7-54 

5 1 5565 

2 

59 

465522 

6*89 

980635 

•64 

484887 

7 • 53 

5 i 5 i i 3 

1 

60 

466935 

6-88 

980096 

• 64 

480339 

7 - 53 

5 i 466 i 

0 


Cosine 

D. 

Sine 


Cotang. 

1 I). 

Tang. 

M. 


(73 DEGREES.) 

















































SINES AND TANGENTS. (17 DEGREES.) 


85 


M. 

Sine 

D. 

Cosine 

D. 

Tang. ; D. 

Cotang. 


1 o 
! i 

2 

0 

o 

4 

5 

6 

7 

8 

y 

10 

i 11 

1 12 

f U 
i i 

1 5 

16 

i? 

*9 

20 

21 

22 

23 

24 

25 

26 

1 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 

48 

49 

5 0 

5 1 

02 

53 1 

54 I 

55 

56 

5 ? 

58 

69 

3 C 

9-465935 

466348 

466761 

467173 

467085 

| 467996 

I 468407 
468817 
469227 
469637 
470046 

9-470455 

470863 

471271 

471679 

472086 

472492 

472898 

4733 o 4 

473710 

474110 

9 - 4745 i 9 

474923 

476327 

475730 

476 r 33 

476536 

476938 

477340 

477741 

478142 

9-478042 

478942 

479342 

479741 

480140 

480539 

480987 

48 i 334 

481731 

482128 

9-482525 
482921 
4833 16 

483712 

484107 
484801 
484895 
486289 
485682 
486076 

9-486467 

486860 

487201 

487643 

488034 

488424 

488814 

489204 

489603 

489982 

6-88 

6-88 

6-87 

6-86 

6-85 

6-85 

6 • 84 
6-83 
6-83 
6-82 

6-8i 

6-80 

6-80 
6-70 
6-78 
6-78 
6-77 
6-76 
6-76 
6-75 
6-74 

6-74 
6- 7 3 
6-72 
6-72 
6-71 
6-70 • 
6-69 
6-69 
6-68 
6-67 

6-67 

6*66 

6-65 

6-65 

6-64 

6-63 

6-63 

6-62 

6-6i 

6 • 61 

6-60 
6-5 9 
6 - 5 9 
6-58 
6*57 
6-57 
6-56 
6-55 
6-55 
6-54 

6-53 

6-53 

6-52 

6 • 5 1 

6 - 5 1 
6 - 5 o 
6 - 5 o 
6-49 
6-48 
6-48 

9-980696 

980508 

980619 

980480 

980442 

980403 

980364 

980320 

980286 

980247 

980208 

9-980169 
980130 
980091 
980062 
980012 
979973 

979934 

979895 

979855 

979816 

9-979776 

979707 

979697 

979668 

979618 

979 5 79 

979539 

979499 

979409 

979420 

9-979380 

979340 

979300 

979260 

979220 

979180 

979140 

979100 

979 o5 9 

979 OI 9 

9-978979 

978939 

978898 

978868 

978817 

978777 

978736 

978696 

978655 

978615 

9-978574 

978533 

978493 

978462 

978411 

978370 

978329 

978288 

978247 

978206 

• 64 
•64 
•65 
•65 
•65 
•65 
•65 
•65 
•65 
•65 
•65 

• 65 
-65 
-65 
-65 
-65 

• 65 

• 66 
• 66 
• 66 
• 66 

• 66 
■ 66 
• 66 
| -66 
! -66 
•66 
• 66 
• 66 
• 66 
• 66 

• 66 
• 66 
.67 
.67 

• 67 
.67 

• 67 

• 67 

• 67 

• 67 

• 67 
.67 
.67 

*? 7 

• 67 

• 67 
.67 

• 68 
• 68 
• 68 

• 68 
• 68 
• 68 
• 68 
• 68 
• 68 
.68 
• 68 
• 68 
• 68 

9 - 4 S 5339 

486791 

486242 

486698 

487143 

487693 

488043 

488492 

488941 

489390 

489838 

9-490286 
490733 
491180 
491627 
49207 3 
492519 
492965 
493410 
493854 
494299 

9-494743 
496r 86 

49563 0 
496073 
4965 i 5 
496957 

497399 

497841 

498282 

498722 

9-499163 

499603 

600042 

5 oo 48 i 

600920 

5 oi 359 

501797 

5 o 2235 

502672 

5 o 3 io 9 

9 - 5 o 3546 

503982 

5 o 44 i 8 

5 o 4854 

500289 

606724 

606169 

5 o 65 g 3 

507027 

507460 

9*507893 

5 o 8326 

608769 

509191 

509622 

5 10064 

5 1 0485 
510916 

5 11 3 46 
611776 

j 7*55 
7-52 

7 • 5 1 

7 • 5 1 
7-5o 

1 7-49 

7-49 
7-48 
7-47 
7-47 
7.46 

7-46 

7.46 

7*44 

7-44 

7-43 

7-43 

7-42 

7.41 

7.40 

7.40 

7.40 

7-39 

7-38 

7-37 

7-37 

7 -36 

7 • 36 
7*35 
7-34 
7-34 

7-33 

7*33 

7-32 

7 * 3 i 

7 * 3 i 

7 * 3 o 

7 * 3 o 

7-20 

7-28 

7.28 

7.27 

7.27 

7-26 

7-25 

7-25 

7-24 

7-24 

7-23 
7-22 
*r -22 

7-21 

7-21 

7-20 

7-19 

7-19 

7<i 5 

7* 18 
7.17 
7-16 
7-16 

io-614661 
514200 

5 1 3756} 

5 13307 

612867 

5 124.07 
5 n 9 5 7 

5 11 5 oS 
5 i1069 

5 10610 
510162 

10*509714 
609267 
508820 
608373 
507927 
607481 
507035 
5 o 65 9 o 
5 o 6 146 
606701 

io- 5 o 5257 
504814 
504370 
5 o 3 9 27 
5 o 3485 
5 o 3 o 43 
5 o 26 oi 
502 1 5 g 
601718 
601278 

10*600837 
5 oo 3 9 7 
499908 
499019 
499080 
498641 
498203 
497765 
497328 
496891 

10-496454 
496018 
495582 
495 146 

494711 

494276 

49884.1 

493.407 ! 

492978 

492540 

[0-492107 
491674 
491241 
490809 
490378 
489946 
48961 5 
489084 
480654 
488224 

60 

$ 

55 
. 64 

53 

I 52 

51 
j 5 o 

i 49 

1 48 
47 

1 46 
i 45 
i 44 

43 

42 

4 i 

40 

3 9 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

10 
l8 

17 

l6 

i 5 

1 4 

>3 

12 1 

11 I 
10 

7 

5 

5 

4 

3 

2 

1 

0 


Connie | 

D. ! Sine 

D. 

Cotang. ! D. i Tang. 

M. 

-.- . 


(72 DEGREES.) 


17 


















































































86 (18 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-489982 

6-48 

9-978206 

-68 

9-511776 

7.16 

10-488224 

60 

1 

490371 

490769 

6-48 

97 8i65 

-68 

512206 

7.16 

487794 

?9 

2 

6-47 

978124 

•68 

512635 

7-13 

487365 

58 

67 

3 

491147 

6-46 

978083 

•69 

5i3o64 

7-U 

486936 

4 

49i535 

6-46 

978042 

•69 

5i3493 

7-U 

486307 

56 

5 

491922 

492308 

6-45 

978001 

•69 

513921 

7 * i3 

486079 

55 

6 

6-44 

977960 

977018 

977877 

•69 

5i4349 

7 * i3 

48565i 

54 

7 

492695 

6-44 

•69 

514777 

7-12 

485223 

53 

6 

493081 

6-43 

•69 

515204 

7-12 

484796 

52 

- 

493466 

6-42 

977835 

-69 

5i5631 

7-u 

484369 

5i 

IC 

49385i 

6-42 

977794 

•69 

516067 

7-10 

488948 

5o 

11 

9-494236 

6-41 

9-977752 

•69 

9-516484 

7-10 

io-4835i6 

49 

12 

49462i 

6 • 41 ' 

977711 

•69 

516910 

7-09 

483090 

48 

13 

14 

495oo5 

495388 

6-40 

6-39 

977660 

977628 

-6 9 

•69 

517335 

517761 

7-00 

7-08 

482665 

482239 

47 

46 

i5 

496772 

6-39 

977686 

•69 

5i8i85 

7-08 

481815 
481390 

46 

16 

496154 

6-38 

977544 

•70 

5i86io 

7.07 

44 

17 

496537 

6-37 

9775o3 

•70 

519034 

519458 

7-06 

480966 

480042 

43 

18 

496919 

6*37 

97746i 

.70 

7-06 

42 

19 

497001 

6-36 

977419 

-70 

519882 

7-o5 

480118 

4i 

20 

497683 

6-36 

977377 

.70 

52o3o5 

7-o5 

479695 

40 

21 

9•498064 

6-35 

9-977335 

•70 

9-620728 

7-04 

10-479272 

478849 

3 9 

22 

498444 

6-34 

977293 

• 70 

521151 

7 -o3 

38 

23 

498825 

6-34 

977251 

•7° 

621673 

7-o3 

478427 

3 7 

24 

499204 

6-33 

977209 

•70 

621996 

7 -o3 

478006 

36 

25 

499684 

6-32 

977167 

•70 

522417 

7-02 

477583 

35 

26 

499963 

6-32 

977125 

.70 

522838 

7-02 

477162 

34 

27 

5oo342 

6 • 31 

977°83 

•70 

523 2 5 9 

7-01 

476741 

33 

28 

500721 

6 * 31 

97704i 

•70 

52368o 

7-oi 

476320 

32 

29 

501099 

6-3o 

976999 

97 6 9 5 7 

•70 

524100 

7-00 

476900 

3i 

3o 

501476 

6-29 

.70 

524520 

6.99 

475480 

3o 

3i 

9-5oi854 

6-29 

9-97 6 9U 

•70 

9-524^39 

6.99 

6.98 

10-476061 

2 9 

32 

5o223l 

6.28 

976872 

•7i 

525359 

525778 

474641 

28 

33 

602607 

6-28 

976880 

•7i 

6.98 

474222 

27 

34 

602984 

6-27 

976787 

•7i 

526197 

6.97 

4738o3 

26 

35 

5o336o 

6-26 

976745 

•7i 

5266i5 

6.97 

473385' 

25 

36 

5o3735 

6-26 

976702 

" l 1 

527o33 

6.96 

472967 

24 

37 

5o4i10 

6-25 

976660 

•7i 

527451 


472049 

23 

38 

5o4485 

6-25 

976617 

.71 

527868 

6- 9 5 

472132 

22 

39 

5o486o 

6-24 

976574 

•7i 

528285 

6- 9 5 

47Hi5 

21 

4o 

5o5234 

6-23 

976532 

.71 

528702 

6.94 

471298 

20 

4i 

9-5o56oS 

6-23 

9.976489 

•7i 

9-5291 19 

529530 

6. 9 3 

10-470881 

IO 

42 

606981 

6-22 

976446 

•7i 

6. 9 3 

470466 

18 

43 

5o6354 

6-22 

976404 

•7i 

529960 

6. 9 3 

47oo5o 

*7 

44 

506727 

6-21 

976361 

•7i 

53o366 

6.92 

469634 

16 

45 

5o7oqq 

6-20 

676318 

•7i 

530781 

6. 9 ! 

469219 

468804 

i5 

46 

607471 

6-20 

976275 

•7i 

531196 

6.91 

14 

47 

607843 

6-19 

976232 

.72 

53i6i1 

6-9° 

468389 

i3 

48 

608214 

6-19 

976189 

•72 

532025 

o-oo 

467973 

467361 

12 

49 

5o8585 

6-18 

976146 

.72 

532439 

532853 

6.89 

11 

5c 

508956 

6-18 

976103 

.72 

6-89 

467147 

10 

5i 

9.509326 

6-17 

9-976060 

.72 

9-533266 

6-88 

10-46673 i 

q 

52 

609696 

6-16 

976017 

•72 

533679 

6-88 

466321 

8 

53 

5ioo65 

6-16 

975974 

.72 

534092 

6.8 7 

46590S 

7 

54 

5io434 

6 • 15 

975930 

• 72 

5345o4 

6-87 

465496 

465 o 84 

6 

55 

5io8o3 

6 -15 

975887 

•72 

534916 

535328 

6-86 

5 

56 

511172 

6-14 

975844 

•72 

6-86 

464672 

4 

57 

51154o 

6 • 13 

975800 

•72 

535739 

6-85 

464261 

? 

58 

511907 

6 • 13 

97 5 757 

•72 

536i5o 

6-85 

46385 o 

n 

4 

5 9 

612275 

6-12 

975714 

.72 

53656i 

6-84 

463439 

T 

60 

512642 

6-12 

975670 

.72 

536972 

6-84 

463028 



Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang, 

I M. 


(71 DECREES.) 


































































SINES AND TANGENTS. (19 DEGREES.) 


37 


M. 

Sine 

D. 

Cosine 

D. 

J Tang. 

D. 

Cotang. 


0 

9-512642 

6-12 

9-975670 

•73 

! 5 536972 

6-84 

10-463028 

60 

i 

5 i 3 oo 9 

6-11 

975627 

•73 

537382 

6-83 

462618 

5 q 

2 

5 i 3375 

6-i 1 

975583 

.73 

537792 

6-83 

462208 

58 

3 

5 i3741 

6-io 

975539 

.7.3 

538202 

6-82 

461708 

01 

4 

514107 

6-09 

976496 

•73 

53 8611 

6-82 

'461389 

56 

5 

514472 

6-o 9 

976462 

- 7 3 

539020 

6 • 81 

460980 

55 

6 

514837 

6-08 

976408 

•73 

539429 

6 • 81 

460071 

54 

7 

5 i 5202 

6-08 

975365 

- 7 3 

539837 

6-80 

4601 63 

53 

8 

5 1 5566 

6-07 

970321 

- 7 3 

540245 

6-80 

459755 

52 

9 

5 i 593 o 

6-07 

975277 

.73 

54 o 653 

6-79 

459847 

5 i 

10 

516294 

6-06 

975233 

.73 

541061 

6-79 

458939 

5 o 

ii 

9-516667 

6 -o 5 

9.975189 

• 73 

9-541468 

6-78 

ic -458532 

49 

12 

517020 

6 -o 5 

976145 

•73 

541875 

6-78 

468125 

48 

i 3 

517382 

6-04 

975101 

-73 

542281 

6-77 

457719 

47 

U 

517745 

j 6-04 

976057 

•73 

642688 

6-77 

457312 

46 

i 5 

518107 

6 -o 3 

975 oi 3 

•73 

648094 

6-76 

456906 

45 

16 

618468 

6 -o 3 

974969 

•74 

543499 

6-76 

456 ooi 

44 

ii 

518829 

6-02 

974920 

•74 

648905 

6-75 

466095 

43 

i8 

519190 

6-ox 

974880 

•74 

5443 10 

6-75 

455690 

42 

*9 

5 i 955 i 

6-oi 

974836 

•74 

5447 i 5 

6-74 

455285 

4 i 

20 

5 i 99 ii 

6-oo 

974792 

•74 

545119 

6-74 

454881 

4 o 

2.1 

9-620271 

6-oo 

9-974748 

•74 

9 545524 

6-73 

10-454476 

39 

22 

52 o 63 i 

5-99 

974703 

•74 

545928 

6-73 

454072 

38 

23 

520990 

5-99 

974669 

•74 

54633 i 

6-72 

453669 

3 ? 

24 

521349 

0-98 

974614 

•74 

546735 

6-72 

453265 

36 

23 

521707 

6-98 

974670 

•74 

647133 

6-71 

452862 

35 

26 

522066 

5-97 

974525 

•74 

547540 

6-71 

462460 

34 

27 

622424 

6-96 

97448 i 

•74 

547943 

6-70 

462067 

33 

28 

522781 

6-96 

974436 

•74 

548345 

6-70 

45 1 655 

32 j 

l 9 

523 i 38 

5-95 

974391' 

•74 

648747 

6-69 

45 i 253 

3 i 

3 o 

523495 

5-96 

974347 

-76 

549149 

6-69 

45 o 85 i 

3 o 

3 i 

9-523852 

5-94 

9-974302 

-75 

9 • 54955 o 

6-68 

io- 45 o 45 o 

29 

32 

624208 

5-94 

974257 

-76 

549951 

6-68 

460049 

28 

33 

524564 

5-93 

974212 

-76 

55 o 352 

6-67 

449648 

27 

34 

624920 

5-93 

974167 

•75 

550762 

6-67 

449248 

26 

35 

626275 

5-92 

974122 

•75 

55 11 52 

6-66 

448848 

25 

36 

52563 o 

5 -gi 

974077 

•75 

55 i 552 

6-66 

448448 

24 

37 

526984 

5 -gi 

974032 

•75 

551952 

6-65 

448048 

23 

38 

626339 

5 -go 

973987 

•75 

55235 i 

6-65 

447649 

22 

3 9 

526693 

5 -go 

973942 

•76 

55275 o 

6-65 

447260 

21 

4 0 

527046 

5-89 

973897 

.70 

553 149 

6-64 

44685 1 

20 

4 i 

9-527400 

.5-89 

9*973852 

•75 

9-553548 

6-64 

10-446452 

19 

42 

627763 

5 • 88 

973807 

•73 

553946 

6-63 

446 o 54 

18 

43 

528 io 5 

5-88 

973761 

• 7 5 

554344 

6-63 

445656 

17 

44 

628468 

5.87 

973716 

.76 

554741 

6-62 

445269 

l6 

45 

528810 

0-87 

973671 

.76 

555 1 3 g 

6-62 

444861 

i 5 

46 

529161 

5-86 

973625 1 

•76 

555536 

6-6i 

444464 

i 4 

47 

5295 i 3 

5-86 

97358 o j 

• 76 

555933 

6-61 

444067 

i 3 

48 

529864 

5-85 

973535 

• 76 I 

556329 

6-60 

443671 

12 

49 

53o2i5 

5-85 

973489 

• 76 

556726 

- 6-60 

443276 

11 

5 o 

53 o 565 

5-84 

973444 

.76 

557121 

6-69 

442879 

10 

5 i 

9-53091 5 

5-84 

9-973398 

.76 

9-557517 

6-59 

10-442483 

9 

52 , 

53 i 265 

5-83 

973352 

.76 

557913 

6-59 

442087 

8 

53 i 

53 1614 

5-82 

973307 

• 76 

5583 o 8 

6-58 

441692 

7 

54 

53 i 9 63 

5-82 

973261 

.76 

558702 

6-58 

441298 

6 

55 

5323 i 2 

5 -81 

973215 

.76 

559097 

6-5 7 

440903 

5 

56 

53266 i 

5 -81 

973169 

.76 

559491 

6-5 7 

440609 

4 

57 

533 oo 9 

5 -80 

973124 

-76 

559885 

6-56 

4401io 1 

3 

58 

533357 

5 -80 

973078 

• 76 

660279 

6-56 

439721 

2 

5 9 

533704 

5.79 

973 o 32 

•77 

660678 

6-55 

439327 j 

1 

60 

534 o 52 i 

1 

5.78 

972986 

•77 

56 1066 

6-55 

43893 J j 

1 

0 


Ccr«ue 1 

D. 

Sine 

D. ! 

Cotang. 

D. 

Tang 1 M. 


(70 DEGREES.) 












































































38 


(20 DEGREES.; A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

c 

9"534o52 

5-78 

I 

O 34399 

5.77 

2 

534745 

5.77 

3 

535092 

5.77 

4 

535438 

5.76 

5 

535783 

5.76 

6 

536129 

5.75 

7 

536474 

5.74 

.8 

5368 18 

5-74 

9 

537i63 

5-73 

10 

537507 

5.73 

11 

9.537851 

5.72 

12 

13 

538194 

538538 

5-72 

5.71 

14 

53888o 

5.71 

i5 

539223 

5.70 

16 

539565 

5.70 

17 

539907 

5*69 

18 

540.249 

5.69 

19 

540590 

5-68 

20 

540931 

5-68 

21 

9.541272 

5-67 

22 

5416 :3 

5.67 

23 

541953 

5-66 

24 

542293 

5-66 

25 

542632 

5-65 

26 

542971 

5-65 

27 

5433 io 

5-64 

28 

543649 

5-64 

3o 

543987 

544320 

5-63 

5-63 

3i 

9 •544663 

5-62 

32 

540OOO 

5-62 

33 

545338 

5-6i 

34 

545674 

5- 61 

35 

546011 

5.6o 

36 

546347 

5.6o 

3 7 

546683 

5.59 

38 

547019 

5-59 

3 9 

547354 

547689 

5-58 

4o 

5-58 

4 1 

9.548024 

5.57 

42 

43 

548359 

548693 

5*57 

5-56 

44 

549027 

5-56 

45 

54936o 

5-55 

46 

549698 

5-55 

47 

560026 

5-54 

48 

55 o 359 

5-54 

49 

550692 

5-53 

5o 

55 io 24 

5-53 

5i 

0•55 1 356 

5-52 

52 

551687 

5-52 

53 

5520i8 

5-52 

54 

552349 

5 • 5 1 

55 

552680 

5 • 5 1 

56 

553oio 

5-5o 

57 

553341 

5-5o 

58 

553670 

0-49 

09 

554 ooo 

5-49 

60 

554329 

5-48 

_ 

Cosine 

D. 


Cosine 


9.972986 

972940 

972894 

972848 

972802 

972700 

972709 

972668 

972617 

972670 

972524 

9.972478 

972431 

972385 

972338 

972291 

972245 

972198 

972161 

972105 

972058 

9.972011 
971964 

97 1 9 I 7 
971870 

971823 

971776 

971729 

971682 

971635 

971588 

9.971540 

971493 

971446 

971398 

97 i 35 i 

97 i3o3 

971256 

971208 

971161 

971113 

9-971066 

971018 

970970 

970922 

970874 

970827 

970779 

970731 

970683 

970635 

9-970586 
970538 
970490 
970442 
970394 
970340 
970297 

970249 

970200 

970,52 

Sine 


D. 


77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

77 

78 
78 
78 
78 
78 
78 
78 
78 
78 

78 

78 

7 « 

78 

78 

78 

79 
79 
79 
79 

79 

79 

79 

79 

79 

79 

79 

79 

79 

79 

80 
80 
80 
80 
80 
80 
80 
80 
80 
80 

80 

80 

80 

80 

80 

81 
81 
81 
81 
81 


Tang. 


9- 56 1066 
56 i 459 
56 1 85 1 
562244 
562636 
563028 
563419 
5638 11 
564202 
564092 
564933 

9.565373 
565763 
566 1 53 
566542 
566932 
567320 
567709 
568 oo 8 
568486 
563873 

9.569261 
569648 
570035 
570422 
570809 
571190 
571 58 1 


072802 

572738 

9.573123 

573507 

573892 

574276 

574660 

675044 

575427 

576810 

576193 

576676 

9.576968 

677341 

577723 

578104 

578486 

678867 

579248 

579629 

680009 

580389 

9.580769 
681149 
581628 
681907 
582286 
582665 
583o43 
583422 
5838oo 
584177 


D. Cotang. 


D. . 

Cotang. 

-—. 

6-55 

10-438934 

60 

6-64 

438041 

09 

6-54 

438149 

58 

6-53 

437766 

5? 

6-53 

437364 

56 

6-53 

436972 

43658i 

55 

6-52 

54 

6-52 

436i8o 

53 

6-5i 

435798 

52 

6 • 5 1 

4354o8 

5i 

6-5o 

435017 

5o 

6-5o 

10-434627 

49 

6-49 

434237 

48 

6-49 

433847 

47 

6*49 

433458 

46 

6.48 

433o68 

40 

6.48 

432680 

44 

6-47 

432291 

43 

6-47 

431902 

42 

6-46 

43i0i4 

41 

6-46 

431127 

4o 

6-45 

10*430739 

3o 

6-45 

43 o 302 

38 

6-45 

429965 

37 

6-44 

429078 

36 

6-44 

6-43 

429191 

4288o5 

35 

34 

6-43 

428419 

33 

6-42 

428o33 

32 

6-42 

427648 

3i 

6-42 

427262 

3o 

6-41 

10-426877 

20 

6-41 

426493 

28 

6-40 

426108 

27 

6*40 

425724 

26 

6-39 

425340 

25 

6*39 

424956 

24 

6.39 

424073 

23 

6-38 

424190 

22 

6-38 

423807 

21 

6A7 

423424 

20 

6-3*7 

io-423o4i 

19 

6-36 

422659 

l8 

6-36 

422277 

I? 

6-36 

421896 

l6 

6-35 

4215i4 

i5 

6-35 

421133 

14 

6-34 

420752 

i3 

6-34 

420371 

12 

6-34 

419991 

11 

6-33 

419611 

10 

6-33 

6-32 

10-419231 

4i885i 

§ 

6-32 

418472 

7 

6-32 

418093 

6 

6 • 3 1 

417714 

5 

6 • 31 

417335 

4 

6-3o 

6-3o 

416957 

416078 

3 

2 

6-29 

416200 

1 

6-29 

415823 

0 

I). 

Tang. 

M. 


(69 DEGREES.) 















































SINES AND TANGENTS. (21 DEGREES.) 


39 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-554329 

5.48 

9.970152 

• 81 

9.584177 

6-29 

io* 4 i 5823 

60 

i 

554658 

3 • 48 

970103 

• 81 

584555 

6-29 

416445 

5 9 

2 

554987 

5-47 

970055 

.81 

684932 

5-28 

4 i 5 o 68 

5 $ 

3 

5553 1 5 

5.47 

970006 

• 81 

5853 og 

6-28 

414691 

57 

4 

555643 

5.46 

969957 

• 81 

585686 

6-27 

4143 l 4 

56 

5 

555971 

5-46 

969909 

• 81 

586062 

6-27 

4 i 3938 

55 

6 

556299 

5-45 

969860 

• 81 

086489 

6-27 

4 i 356 i 

54 

7 

556626 

5-45 

969811 

• 8i 

5868 1 5 

6-26 

41 3 1 85 

53 

8 

556953 

5-44 

969762 

• 81 

587190 

6*26 

412810 

52 

9 

557280 

5-44 

969714 

• 81 

587666 

6-25 

4 12434 

5 i 

IO 

557606 

5-43 

969665 

• 81 

587941 

6-25 

412059 

5 o 

11 

9.557932 

5-43 

9.969616 

.82 

9• 5 S 83 16 

6-25 

10-411684 

49 

12 

558258 

5-43 

969667 

.82 

588691 

6-24 

411309 

48 

i 3 

558583 

5-42 

969618 

•82 

589066 

6-24 

410934 

47 

i i 

558909 

5.42 

969469 

.82 

589440 

6-23 

410060 

46 

15 

559234 

5.41 

969420 

.82 

589814 

6-23 

410186 

45 

l6 

55 9 558 

5.41 

969370 

• 82 

590188 

6-23 

409812 

44 

17 

55 9 S 83 

5.40 

9693 21 

•82 

590662 

6-22 

409438 

43 

18 

560207 

5-40 

969272 

•82 

590935 

6-22 

4 ooo 65 

42 

19 

56 o 53 i 

5 - 3 9 

969223 

• 82 

691308 

6-22 

408692 

4 i 

20 

56 o 855 

5.39 

969173 

• 82 

691681 

6-21 

408319 

40 

21 

9-56i178 

5-38 

9.969124 

.82 

9-692054 

6-21 

10-407946 

3 9 

22 

56 i 5 oi 

5-38 

969075 

• 82 

592426 

6*20 

407574 

38 

23 

561824 

5-37 

969025 

• 82 

692798 

6-20 

407202 

3 7 

24 

562146 

5-37 

968976 

• 82 

593170 

6*19 

406829 

36 

25 

562468 

5-36 

968926 

.83 

5 g 3542 

6* 19 

406458 

35 

26 

562790 

5-36 

968877 

• 83 

693914 

6.18 

406086 

34 

27 

563 ii 2 

5-36 

968827 

• 83 

694285 

6.18 

40571 5 

33 

28 

563433 

5-35 

968777 

• 83 

5 g 4656 

6-18 

4^5344 

32 

29 

563755 

5-35 

968728 

.83 

696027 

6-17 

404973 

3 i 

3 o 

564075 

5-34 

968678 

• 83 

596898 

6-17 

404602 

3 o 

3 i 

9.564396 

5-34 

9.968628 

• 83 

9.695768 

6-17 

10*4042 3 2 

29 

32 

564716 

5-33 

9 685 7 8 

• 83 

696133 

6-16 

4o3862 

28 

33 

565 o 36 

5.33 

9 685 2S 

•83 

696508 

6* 16 

403492 

27 

34 

565356 

5*32 

968479 

• 83 

696878 

6-16 

4 o 3 l 22 

26 

35 

566676 

5-32 

968429 

• 83 

597247 

6 • 1 5 

402753 

20 

36 

566996 

5 ■ 3 1 

968379 

• 83 

697616 

6 • 1 5 

402384 

24 

? 7 

5663 i 4 

5 • 3 1 

968829 

• 83 

597935 

6 • 1 5 

4 o 2 oi 5 

23 

38 

566632 

5 - 3 1 

968278 

• 83 

698354 

6* 14 

401646 

22 

3 9 

566961 

5 - 3 o 

968228 

•84 

698722 

6-14 

401278 

21 

4 o 

567269 

5 - 3 o 

968178 

•84 

599091 

6 * i3 

400909 

20 

4 i 

9.567587 

0-29 

9.968128 

.84 

9-599469 

6 * 1 3 

10.400641 

19 

42 

567904 

5*29 

968078 

.84 

599827 

6 • 1 3 

400173 

18 

43 

568222 

5-28 

968027 

•84 

600194 

6-12 

399806 

17 

44 

568539 

5-28 

967977 

.84 

600662 

6-12 

399438 

l6 

43 

568856 

5-28 

967927 

.84 

600929 

6-11 

399071 

i 5 

46 

569172 

5-27 

967876 

.84 

601295 

6-11 

398704 

14 

47 

569488 

5-27 

967S26 

.84 

601682 

6-11 

3 9 8338 

i 3 

48 

569804 

5*26 

967775 

.84 

602029 

6-10 

397971 

12 

49 

570120 

5-26 

967725 

.84 

602396 

6* 10 

897605 

11 

5 o 

570435 

5-25 

967674 

• 84 

602761 

6-io 

397289 

10 

5 i 

9070751 

5-25 

9-967624 

.84 

9-6o3i27 

6-09 

10-396873 

9 

52 

571066 ! 

5-24 

967573 

.84 

6 o 34 g 3 

6-09 

096507 

8 

03 

5 7 i 38 o j 

5-24 

967622 

.85 

6 o 38 o 8 

6-09 

896142 

7 

54 

671696 

5-23 

967471 

.85 

604223 

6-08 

39^777 

6 

55 | 

572009 

5-23 

967421 

• 85 

6 o 4588 

6-08 

396412 

0 

56 

5 7 2323 | 

5-23 

967370 

• 85 

604953 

6-07 

396047 

4 

rl 

672636 ! 

5-22 

967319 

• 85 

6 o 53 i 7 

6-07 

3 9 4683 

3 

58 

572960 

5*22 

967268 

• 85 

6 o 568 a 

6-07 

3 9 43 i 8 

2 

59 ! 

5 7 3263 

5-21 

967217 

• 85 

606046 

6-06 

393964 

1 

60 1 

[ 

573575 

5-21 

967166 

• 85 

1 

606410 

6-06 

893090 

0 

_ 

Cosine 

D. 

Sine 

D. ! 

Cotang. 

D. 

Tang. 

JL 


(68 DEGREES.) 
























































I 


40 


(22 DECREES.) A TABLE OF LOGARITHMIC 


|~M.~ 


D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


5-21 

9-967166 

.85 

9-606410 

6.06 

10-393590 

60 

5-20 

967116 

-85 

606773 

6-06 

393227 

5 9 

5-20 

967064 

• 85 

607137 

6 -o 5 

! 3 9 2863 

58 

5-19 

967013 

-85 

607500 

6 -o 5 

1 392600 

57 

5 -19 

966961 

• 85 

607863 

6-04 

392137 

56 

5 -i 9 

966910 

• 85 

608225 

6-04 

391775 

55 

5 -18 

5 -18 

966809 

966808 

• 85 

• 85 

6 o 8588 

608960 

6-04 

6 -o 3 

391412 

391060 

54 

53 

•>•17 

966756 

• 86 

609312 

6 -o 3 

390688 

52 

5 -i 7 

966705 

• 86 

609674 

6 o 3 

390326 

5 i 

5 -16 

966653 

• 86 

6 ioo 36 

6-02 

389964 

5 o 

5 -16 

9-966602 

•86 

9-610397 

6-02 

10 389603 

49 

5 -16 

966050 

•86 

610769 

6-02 

389241 

38888 o 

48 

5 -1 5 

966499 

-86 

611120 

6-oi 

47 

5-15 

966447 

-86 

611480 

6-oi 

388520 

46 

5 -14 

966395 

-86 

611841 

6-oi 

388169 

45 

5 -14 

966344 

• 86 

612201 

6-oo 

387799 

44 

5-13 

966292 

• 86 

6 i 256 i 

6-oo 

3874)9 

43 

5 -1 3 

’966240 

• 86 

612921 

6-oo 

387079 

42 

5-13 

966188 

• 86 

613281 

5-99 

386719 

4 i 

5-12 

9661 36 

• 86 

6 i 364 i 

5.99 

38635 9 

40 

5-12 

9-966086 

.87 

9*614000 

5-98 

10• 386 ooo 

39 

5 -n 

966033 

.87 

614359 

5.98 

385641 

38 

5 . XI 

965981 

.87 

614718 

5- 9 8 

385282 

37 

5 .11 
5 -io 

965928 

965876 

.87 

•87 

615077 
61 5435 

5-97 

5.97 

384923 

384565 

36 

35 

5 -io 

965824 

•87 

615793 

5.97 

384207 

34 

5.09 

965772 

•87 

616101 

5-96 

383849 

33 

5.09 

965720 

•87 

616509 

5-96 

383491 

32 

5.09 

965668 

.87 

616867 

5.96 

383 1 33 

3 i 

5 -08 

966616 

.87 

617224 

5.95 

382776 

3 o 

5 - 08 

9-965563 

.87 

9-617582 

5-95 

10-382418 

29 

5-07 

9655 ii 

.87 

617939 

5- 9 5 

382061 

28 

5-07 

965458 

•87 

618295 

5-94 

381705 

27 

5 -06 

965406 

.87 

61 8652 

5-94 

38 i 348 ■ 

26 

5 -06 

965353 

• 88 

619008 

5-94 

380992 

25 

5 -06 

9653 oi 

• 88 

619364 

5- 9 3 

38 o 636 

24 

5 -o 5 

965248 

• 83 

619721 

5- 9 3 

380279 

23 

5 -o 5 

965195 

• 88 

620076 

5- 9 3 

379924 

22 

5 -o 4 

965 i 43 

• 88 

620432 

5-92 

879068 

21 

5 -04 

965090 

• 88 

620787 

5-92 

379213 

20 

5 -o 3 

9-965037 

• 88 

9-621142 

6-92 

io -378858 

IO 

,^ 5 -o 3 

964984 

• 88 

621497 

5-91 

3785 o 3 

l8 

■ 5 -o 3 

964931 

• 88 

621862 

5*91 

378148 

17 

5-02 

964879 

• 88 

622207 

5*90 

377793 

l6 

5-02 

964826 

• 88 

622661 

5-90 

377439 

i 5 

5 -oi 

964778 

• 88 

622915 

5 -ao 

077085 

1 4 

5 -oi 

964719 

• 88 

623269 

623623 

5.89 

376731 

i 3 

5 -oi 

964666 

• 89 

5.89 

376377 

12 

5 -oo 

964613 

• 89 

623976 

5-89 

376024 

11 

5 -oo 

964060 

•89 

6243)0 

5-88 

375670 

10 

4-99 

9•964507 

.89 

9-624683 

5-88 

10-376317 

9 

4-99 

964454 

• 89 

625 o 36 

5-88 

374964 

8 

4-99 

964400 

.89 

625388 

5-87 

374612 

7 

4-98 

964347 

•89 

626741 

6-87 

374259 

6 

4-98 

964294 

• 89 

626093 

5-87 

373907 

373555 

5 

4-97 

964240 

•89 

626445 

5-86 

4 

4-97 

964187 

.89 

626797 

5-86 

373203 

3 

4-97 

964133 

•89 

627149 

5-86 

372851 

2 

4-96 

964080 

• 89 

627601 

5-85 

372499 

1 

4-96 

964026 

.89 

627862 

5-85 

372148 

0 

I). 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


Sine 


2 

3 

4 

5 

6 

7 

8 

9 

10 

11 
12 
i 3 
H 

1 5 

16 

17 

18 

*9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

8 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

4 0 

4 1 

42 

43 

44 

45 

46 

47 
43 

to 

5 1 

52 

53 

54 
! 55 
i 56 
i 5 7 
I 58 
1 39 
i 60 


9-573575 

573888 

574200 

574512 

574824 

575i36 

575447 

575758 

576069 

676379 

576689 

9-676999 

577809 

577618 

677927 

578236 

578545 

5 7 8853 

579162 

579470 

5 79777 

9 * 58 oo 85 
680392 
580699 
58 ioo 5 
58 i 3 i 2 
5 S1618 
681924 
682229 
582535 
582840 

9• 583 i 45 
583449 
583754 
584 o 58 
58436 i 
584665 
584968 
686272 
585574 
585877 

9•586179 
686482 
586 7 83 
687085 
58 7 386 
58 7 688 
587989 
088289 
588690 
588890 

9-589190 

589489 

589789 

590088 

590387 

590686 

590984 

591282 

591080 

591878 


Cosii e 


(87 DEGREES.) 
























































I 


SINES AND TANGENTS. (23 DEGREES.) 41 


M. 


Sine 


D. 


Cosine D. 


Tang. 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 
12 

1 3 

14 
ID 

16 

l l 

18 

'9 

20 

2! 

22 

23 

2-i 

2 D 

26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 
33 

36 

37 

38 

39 

4 0 

4 1 

42 

43 

44 
43 

46 

47 

48 

4 9 

5 0 

5 1 

52 

53 

54 

55 

56 
5 ? 

58 

5 9 

60 


9.59187s 

592176 

592473 
592770 
5 9 3 o 67 
5 9 3363 
5 9 3659 
593960 
5 9 425 1 
5 9 4 D 47 
594842 

9.595137 
5 9 5432 
595727 
596021 
5 9 63 1 5 
596609 
59690) 
597196 
597490 
597783 

9.59807 5 
598368 
598660 
5 9 8 9 52 
699244 
5 99 536 
599827 
600i18 
600409 
600700 

9-600990 
601280 
601670 
601860 
6021 5 o 
602439 
602728 
608017 
6 o 33 o 5 
603594 

9 - 6 o 3882 

6 o4«]o 

604457 

604745 

6 o 5 o 32 

6 o 53 i 9 

6 o 56 o 6 

606892 

606179 

606465 

9-606751 
607036 
607322 
607607 
607892 
608177 
60846i 
608745 
609029 
60931 3 


4.96 
4- 9 5 
4- 9 5 
4- 9 5 
4- 9 4 
4- 9 4 
4- 9 3 
4- 9 3 
4- 9 3 
4 • 92 
4.92 

4-91 

4 - 9 i 

4 - 9 i 

4-90 

4-90 

4 - 8 q 

4-89 

4-89 

4-88 

4-88 

4-87 

4 - 8 7 

4-87 

4-86 

4-86 

4-85 

4-85 

4-85 

4.84 

4-84 

4-84 

4-83 

4-83 

4-82 

4-82 

4-82 

4-81 

4-8i 

4*81 

4 -80 
4-80 
79 
79 
79 
78 
78 
78 


4 
4 
4 
4 
4 
4 
4*77 
4-77 
4-76 


■76 

76 

'75 

'75 

•74 

’74 

■74 

'73 

'73 

■73 


9.964026 

963972 

963919 

9 63865 

9 638 ii 

963767 

963704 

963600 

963596 

963542 

963488 

9.963434 
963379 
963320 
963271 
963217 
963 1 63 
963108 
963004 
962999 
962945 

9-962890 

962836 

962781 

962727 

962672 

962617 

962.062 

962008 

9 62453 

96239S 

9-962343 

962288 


962178 i 
96212 3 
962067 . 
962012 ; 
961907 : 
961902 
961846 ; 

9-961791 ! 
961735 j 
961680 
961624 
961669 
961513 
961453 
961402 
961346 
961290 

c- 9 6 i 235 
961179 
96112) 
961067 
961011 
960955 | 
960899 ! 
960843 

960786 
960730 j 


•89 

#1 

90 ; 

■ 90 1 
.90 
.90 
.90 
.90 
.90 

.90 9 

.90 
.90 
.90 
.90 
•90 
.91 

•9 1 

.91 
.91 


.91 

.91 
.91 
■ 91 

• 91 
.91 

• 91 

• 91 
.91 
.92 

• 92 
.92 
.92 
.92 
.92 
.92 

• 92 
•92 
•92 
.92 

•92 

.92 

.92 

■ 9 ? 

• 9 3 

•93 

• 9 3 

• 9 3 

• 9 3 

• 9 3 

•93 

•93 

•93 

•93 

• 9 3 

• 93 

• 9 3 
•94 | 
.94 

.94 


D. 


Cotang. 


627862 
628203 
628554 
628905 
629255 
629606 
629966 
63 o 3 o 6 
63 o 656 
63 ioo 5 
63 1 355 

631704 
632053 
632401 
632760 
633 o 9 8 
633447 
633795 
634143 

6344 9 o 

634838 

9• 635 i 85 
635532 
635879 
636226 
636572 

636919 

637260 

637611 

687956 

638302 

9-638647 
638992 
639337 
639682 
640027 
640371 
640716 
641060 
641 4 o 4 

641747 

9-642091 

642434 

642777 

643120 

643463 

643806 

644148 

644490 

644832 

645174 

9 . 6455 i 6 

645357 

646199 

646040 

646881 

647222 

647662 

647903 

648243 

648583 


5-85 

5-85 

5-85 

5-84 

5-84 

5-83 

5-83 

5-83 

5-83 

5-82 

5.82 

5-82 
5*8i 
5 • 81 
5 • 81 
5 -80 
5* 80 
5-80 
5-79 
5-79 

5-79 


7 o 

■78 

.78 

•11 

11 


5-77 
5-77 


■ 76 

■ 76 
.76 

75 

75 

75 

74 

74 

74 

73 


5-73 

5-73 

0-72 


— 


72 
72 
72 
7 i 
7 i 
7 i 
5-70 
5-70 
5.70 
5-69 

5 - 6 9 
5 -69 
5-69 
5-68 
5-68 
5-68 
5-67 
5*67 
5*67 
5-66 


10-372148 

371797 

371446 

371095 

370745 

370)94 

370044 

369694 

36 9 344 

368 99 5 

368645 

(10*368296 

367947 

367099 
367260 
366902 
366553 
366205 
365857 
3655 10 
365 162 

io.. 3648 i 5 

364468 

364121 

363774 

363428 

363 o 8 i 

362735 

362)89 

362044 

361698 

io- 36 i 353 

36 ioo 8 

36 o 663 

36 o 3 i 8 

369973 

359629 

359284 

358940 

358596 

358253 

10-307909 
357566 
357223 
35688 o 
35652 
356 iq 4 
355802 
355 oio 
355 168 
354826 

10-354484 

354143 
3538 oi 
) 5346 o 
353 119 
352778 
352438 
352097 
351757 
35 i 4 i 7 


60 


Cosine 


D. 


Siive ■ D. ! Cotang. 


D. 


Tang. 


57 

56 

55 

54 

53 

52 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

i 0 

14 
i 3 
12 
11 

10 


7 

6 

5 

4 

3 

2 

1 

o 

M. 


(66 DEGREES.) 



















































































42 


(24 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

— 

0 

9*609353 

4*73 

9*960730 

•94 

9*648583 

5*66 

io*35i4i7 

60 

i 

609697 

4*72 

960674 

•94 

648923 

5*66 

351077 

5o 

2 

609880 

4-72 

960618 

•94 

649263 

5*66 

300737 

53 | 

3 

610164 

4*72 

960661 

•94 

649602 

5*66 

300398 

57 

4 

610447 

4*71 

960006 

•94 

649942 

5*65 

300008 

56 

5 

610729 

4-7 1 

960448 

•94 

65o28i 

5*65 

349719 

50 

6 

611012 

4*70 

960392 

•94 

65o62c 

5*65 

349880 

54 i 

7 

611294 

4-70 

96o335 

•94 

650969 

5*64 

349041 

53 

8 

611676 

4*70 

960279 

•94 

601297 

5*64 

348703 

52 

9 

611808 

4.69 

960222 

•94 

651636 

5*64 

348364 : 

5i 

IO 

612140 

4*69 

960165 

•94 

651974 

5*63 

348026 

5o 

11 

9*612421 

4*69 

9*960109 

• 9 5 

9*652312 

5*63 

10*347688 

49 

12 

612702 

4*68 

960062 

.90 

65265o 

5*63 

34735o 

48 

i3 

612983 

. 4-68 

969996 

.90 

652988 

5*63 

347012 

47 

i4 

613264 

4*67 

969908 

.90 

653326 

5*62 

346674 

46 

i5 

6i3545 

4-67 

969882 

.90 

653663 

5*62 

346337 

45 

i6 

613826 

4*67 

959826 

* 9 5 

654ooo 

5*62 

346000 

44 

17 

6i4io5 

4*66 

959768 

* 9 5 

654337 

5 - 61 

345663 

43 

18 

614385 

4*66 

959711 

* 9 5 

654674 

5 - 61 

345326 

42 

19 

6i4665 

4*66 

959654 

* 9 5 

655oi1 

5 • 61 

3449 8 9 

4i 

20 

614944 

4*65 

909596 

.90 

655348 

5 - 61 

344652 

40 

21 

9-615223 

4*65 

9*969539 

* 9 5 

9•655684 

5*60 

10*344316 

3 9 

22 

6i55o2 

4*65 

959482 

* 9 5 

656o2o 

5* 60 

343980 

38 

23 

615781 

4-64 

o5o425 

.90 

656356 

5* 60 

343644 

37 

24 

616060 

4*64 

9 5 9 368 

•9 5 

656692 

5*69 

3433o8 

36 

25 

6i6338 

4-64 

969310 

.96 

657028 

5*09 

342972 

35 

26 

616616 

4*63 

909253 

.96 

667364 

5*59 

342636 

34 

27 

616894 

4*63 

969196 

.96 

657699 

5*69 

3423oi 

33 

28 

617172 

4-62 

969138 

.96 

653oJ4 

5*58 

341966 

32 

29 

617460 

4-62 

959081 

.96 

658369 

5*58 

341631 

3i 

3o 

617727 

4-62 

959023 

•96 

668704 

5*58 

341296 

3o 

3i 

9•618004 

4*6i 

9•968965 

.96 

9*659039 

5*58 

10*340961 

2 9 

32 

618281 

4*6i 

958908 

.96 

669373 

5*57 

340627 

28 

33 

618558 

4* 61 

95885o 

.96 

669708 

5*57 

340292 

27 

34 

6i8834 

4* 60 

968792 

.96 

660042 

5*57 

339968 

26 

35 

619110 

4* 60 

968734 

.96 

660376 

5*57 

339624 

25 

36 

619386 

4* 60 

968677 

.96 

660710 

5*56 

339^90 

24 

37 

619662 

4*59 

968619 

.96 

661043 

5*56 

338907 

23 

38 

619938 

4-5 9 

958561 

•96 

661377 

5*56 

338623 

22 

3 9 

620213 

4*59 

9585o3 

•97 

661710 

5*55 

338290 

21 

4o 

620488 

4*58 

958445 

•97 

662043 

5*55 

337967 

20 

4i 

9*620763 

4*58 

9*958387 

*97 

9*662376 

5*55 

10*337624 

IO 

42 

62io38 

4*67 

908329 

•97 

662709 

5*54 

337291 

IO 

43 

621313 

4*07 

968271 

•97 

663o42 

5*54 

336908 

17 

44 

621687 

4-67 

958213 

•97 

663375 

5*54 

336625 

16 

4 J 

621861 

4*56 

958i54 

•97 

663707 

5*54 

336298 

i5 

46 

022135 

4*56 

968096 

•97 

664039 

5*53 

335961 

i4 

47 

622409 

4*56 

958o33 

•97 

664371 

5*53 

335629 

i3 

43 

622682 

4*55 

967979 

•97 

664703 

5*53 

335297 

12 

49 

622956 

4*55 

907921 

•97 

665o35 

5*53 

334965 

11 

5o 

623229 

4*55 

907863 

•97 

665366 

5*52 

334634 

10 

5i 

9*6235o2 

4*54 

9*957804 

•97 

9*666697 

5*52 

io*3343o3 

9 

5i 

623774 

4*54 

957746 

.98 

666029 

5*52 

333971 

8 

53 

624047 

4*54 

957687 

•98 

66636o 

5 - 51 

333640 

7 

54 

624319 

4*53 

957628 

.98 

666691 

5 • 51 

333309 

6 

55 

624091 

4*53 

q5i5io 

• 98 

667021 

5 - 51 

332979 

5 

56 

624863 

4-53 

907011 

.98 

667352 

5*5i 

332648 

4 

5 7 

625135 

4*52 

957402 

.98 

667682 

5*5o 

332318 

3 

58 

626406 

4*52 

967393 

*98 

6680i3 

5*5o 

331987 

2 

59 

626677 

4*52 

907330 

.98 

663343 

5*5o 

331667 

1 

60 

625948 

4 ‘ 5 i 

967276 

.98 

668672 

5*5o 

I 331328 

0 


Cosine 

D. 

Sine 

I). 

1 Cotang. 

D. 

Tang. 

! M. 


(65 DEGREES.) 






























































SINES AND TANGENTS. '25 DEGREES.; 


43 


M. 

Sine 

D. 

i 

Cosine 

D. 

Tang. 

| D. 

! Cotang. : 

0 

j 9*625948 

4 * 51 

9*957276 

.98 

9*668673 

5 * 5 o 

io* 33 i 327 

60 

i 

626219 

4 * 5 i 

907217 

*98 

669002 

5*49 

330Q98 

59 

i 

626490 

4 • 5 l 

957168 

• 98 

669332 

5*49 

33 o 663 

53 

3 

626760 

4 * 5 o 

907099 

•98 

669661 

5 * 4 o 

33 o 339 

5 i 

4 

j 627030 

4 * 5 o 

957040 

•98 

66999 r 

5*48 

330009 

56 

5 

627300 

4 * 5 o 

956981 

.98 

670320 

5*48 

329680 

55 

6 

627670 

4*49 

906921 

•99 

670649 

5*48 

329351 

54 

7 

627840 

4*49 

956862 

•99 

670971 

5*48 

329023 

53 

8 

628109 

4*49 

906803 

•99 

671306 

5*47 

328694 

52 

9 

628378 

4*48 

966744 

*99 

6 ii 634 

5*47 

328366 

5 i 

to 

628647 

4*48 

966684 

•99 

67:963 

5*47 

328037 

5 o 

ii 

I 9-628916 

4*47 

9*956625 

•99 

9*672291 

5*47 

10*327709 

49 

12 

629185 

4-47 

966066 

•99 

672619 

5*46 

327381 

48 

i 3 

629453 

4*47 

9565 o 6 

•99 

672947 

' 5*46 

327053 

47 

1 4 

629721 

4.46 

906447 

•99 

673274 

5*46 

326726 

46 

i 5 

629989 

4*46 

966387 

•99 

673602 

5*46 

326398 

45 

16 

630267 

4*46 

956327 

•99 

673929 

5*45 

326071 

44 

17 

630624 

4.46 

966268 

•99 

674267 

5*45 

326743 

43 

18 

630792 

4*45 

966208 

I *00 

674584 

5*45 

326416 

42 

19 

63 1009 

4*40 

906148 

1 *oo 

674910 

5*44 

325090 

4 i 

20 

63 1 326 

4*43 

966089 

1 *00 

675237 

5*44 

324763 

40 

21 

9• 63 1 5 g 3 

4*44 

9*966029 

I *00 

9*675564 

5*44 

io *324436 

39 

22 

631859 

4*44 

960969 

I *00 

675890 

5*44 

324110 

38 

23 

632125 

4*44 

966909 

1*00 

676216 

5*43 

323784 

37 

24 

632392 

4*43 

960849 

I *00 

676643 

5*43 

323467 

36 

25 

632658 

4*43 

905789 

I *00 

676869 

5*43 

323 1 3 1 

35 

26 

632923 

4*43 

966729 

I *00 

677194 

5 * 4.3 

322806 

34 

27 

633 i 8 9 

4*42 

955669 

I *oo 

677020 

5*42 

322480 

33 

28 

633454 

4*42 

900609 

I *00 

677846 

5*42 

322164 

32 

29 

633719 

4*42 

955548 

I *oo 

678171 

5*42 

321829 

3 i 

3 o 

633984 

4 * 4 i 

955488 

1 *00 

678496 

5*42 

32 i 5 o 4 

3 o 

3 i 

9*634249 

4 * 4 i 

9*955428 

1 *01 

9*678821 

5 * 4 i 

10*321179 

29 

32 

6345 i 4 

4 * 40 

9 553 68 

I *01 

679146 

5 • 41 

320854 

28 

33 

63477 s 

4 * 4 o 

955307 

I *01 

679471 

5 * 4 i 

320529 

27 

34 

635 o 42 

4 * 4 o 

955247 

1 *01 

679795 

5 * 4 i 

320205 

26 

35 

6353 o 6 

4*39 

966186 

I *01 

680120 

5 * 40 

319880 

25 

35 

635570 

4*39 

955126 

1*01 

680444 

5 * 4 o 

319506 

24 

37 

635834 

4*39 

955 o 65 

I *01 

680768 

5 • 40 

319232 

23 

38 

636097 

4*38 

955 oo 5 

1*01 

681092 

5 * 4 o 

3 18908 

22 

39 

636360 

4*38 

964944 

1*01 

681416 

5 * 3 9 

3 i 85 S 4 

21 

4 o 

636623 

4*38 

954883 

I *01 

681740 

5 * 3 9 

3 i? 26 o 

20 

4 i 

9-636886 

4*37 

9*954823 

I *01 

9*682063 

5 * 3 9 

10*317937 

19 

42 

637148 

4*37 

954762 

1*01 

682387 

5 * 3 9 

317613 

l8 

43 

637411 

4*37 

964701 

I *01 

682710 

5*38 

317290 

17 

44 

637673 

4*37 

964640 

1*01 

683 o 33 

5-38 

316967 

l6 

45 

637935 

4*36 

904579 

1*01 

683356 

5*38 

316644 

i 5 

46 

638197 

4*36 

904518 

I *02 

683679 

5*38 

3 1 632 1 

1 4 

47 

638458 

4*36 

964467 

I *02 

684001 

• 5 - 37 

3 16999 

1 3 

48 

638720 

4*35 

904896 

1 *02 

684824 

5*37 

3 15676 

12 

49 1 

638981 

4-35 

904335 

I *02 

684646 

5*37 

3 1 5354 

11 

5 o 

639242 

4-35 

904274 

I *02 

684968 

5*37 

3 i 5 o 32 

10 

5l 

9*639003 

4*34 

9*904213 

1*02 

9*680290 

5*36 

10*314710 

9 

5 2 

639764 

4*34 

964152 

I *02 

6856 12 

5*36 

314388 

8 

53 

640024 

4*34 

904090 

I *02 

686934 

5*36 

3 14066 

7 

54 

640284 

4*33 

954029 

I *02 

686255 

5*36 

3 13745 

6 

55 

640544 

4*33 

953968 

I *02 

686577 

5*35 

3 1 3423 

5 

56 I 

640804 

4*33 

963906 

I *02 

686898 

5*35 

3 1 3 i02 

4 

57 

641064 

4*32 

953845 

1*02 

687219 

5*35 

312781 

3 

53 

641324 

4*32 

903783 

I *02 

687540 

5*35 

3 12460 

2 

D9 

641584 

4*32 

953722 

I *o 3 

687861 

5*34 

3 12139 

1 

60 

641842 

4 • 3 1 

95366 o 

I *o 3 

68S182 

5*34 

3 11Si 8 

0 


Cosine 

D. 

Sine 

D. i 

Cotang. 

D. 

Tans’. 

M. 


(G t DEGREES.) 







































































44 


(26 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 

j 

0 

9-641842 

4 - 3 i 

9-953660 

1 -o 3 

9-688182 

5.34 

io- 3 i1818 

60 ; 

l 

642101 

4 - 3 1 

953599 

1 -o 3 

688602 

5-34 

311498 ' 

& 1 

2 

642360 I 

4- 31 

953537 

1 -o 3 

688823 

5-34 

311177 | 

j 8 j 

3 

642618 

4 - 3 o 

953476 

1 -o 3 

689143 

5-33 

810867 1 

57 

4 

642877 

4 - 3 o 

9534 i 3 

1 -o 3 

689463 

5-33 

3 1 0637 I 

56 I 

5 

643 1 35 

4 - 3 o 

953352 

1 -o 3 

689783 

5-33 

310217 ; 

55 

6 

643393 

4 - 3 o 

963290 

1 -o 3 

690103 

5-33 

309897 

54 

7 

643650 

4-29 

953228 I 

1 -o 3 

690423 

5-33 

309677 

53 

8 

643908 

4-29 

953166 

1 -o 3 

690742 

5-32 

309268 

52 

9 

644 i 65 

4-29 

953104 

1 -o 3 

691062 

5-32 

008933 

5 i 

IO 

644423 

4-28 

953042 

1 -o 3 

691381 

5-32 

308619 

5 o 

n 

9-644680 

4-28 

9-962980 

1 -04 

9-691700 

5 • 3 1 

io- 3 o 83 oo 

49 

12 

644936 i 

4-28 

952918 

1 -04 

692019 

5 • 3 1 

307981 

48 

i 3 

645 (o 3 

4-27 

952855 

1 -04 

692338 

5 • 3 1 

307662 

47 

U 

645450 

4-27 

952793 

1 -04 

692666 

5 • 3 1 

307844 

46 

i 5 

645706 

4-27 

952781 

1 • 04 

692975 

5 - 3 1 

307025 

45 

16 

646962 

4-26 

962669 

1 -04 

698298 

5 - 3 o 

306707 

44 

17 

646218 

4-26 

952606 

1 -04 

693612 

5 - 3 o 

3 o 6388 

43 

18 

646474 

4-26 

962044 

1-04 

693930 

5 - 3 o 

306070 

42 

19 

646729 

4-25 

952481 

1 -04 

694248 

5-36 

3 o 5752 

4 i 

20 

646984 

4-25 

962419 

.•04 

694666 

6-29 

806434 

40 

21 

9-647240 

4-25 

9-952366 

1 -04 

9-694883 

6-29 

io- 3 o 6 i17 

3 o 

22 

647494 

4-24 

962294 

1 -04 

695201 

5-29 

3o4799 

38 

23 

647749 

4-24 

962231 

1 -o 4 

696618 

5-29 

304482 

37 

24 

648004 

4-24 

962168 

j -o 5 

6 9 5836 

6-29 

304164 

36 

25 

648208 

4-24 

962106 

1 -o 5 

6961 53 

5-28 

3o3847 

35 

26 

648012 

4-23 

962043 

1 -o 5 

696470 

5-28 

3 o 353 o 

04 

2 7 

648766 

4-23 

961980 

1 -o 5 

696787 

5-28 

3 o 32 i 3 

33 

28 

649020 

4-23 

9 5i 9 t 7 

1 -o 5 

697103 

5-28 

3 o 2 q 97 

32 

29 

649274 

4-22 

95 1 854 

1 -o 5 

697420 

5-27 

3 o 258 o 

3 i 

3 o 

649527 

4- 22 

961791 

1 -o 5 

697736 

5-27 

302264 

3 o 

3 i 

9-649781 

4-22 

9-961728 

1 -o 5 

9-698063 

5-27 

10*3019^7 

29 

32 

65 oo 34 

4-22 

961665 

1 -o 5 

608369 

5-27 

3 oi 63 i 

28 

33 

650287 

4-21 

961602 

.1 -o 5 

698686 

5-26 

3 01 3 1 5 

2 7 ; 

34 

65 o 539 

4-21 

951639 

1 -o 5 

699001 

5-26 

300999 

26 j 

35 

650792 

4-21 

961476 

1 -o 5 

699316 

5-26 

3 oo 684 

25 | 

36 

651044 

4-20 

961412 

1 -o 5 

69963 2 

5-26 

3 oo 368 

24 

3 7 

651297 

4- 20 

951849 

1 -06 

699947 

5-26 

3 ooo 53 

2.3 

38 

65 1549 

4-20 

961286 

1 -06 

700263 

5-25 

299737 

22 

3 9 

65 1800 

4 -19 

951222 

1 -06 

700678 

5-25 

299422 

1 21 

4 o 

652052 

4 -19 

951169 

1 -06 

700893 

5-25 

299107 

20 

4 i 

9 *652804 

4-19 

9-961096 

1 -06 

I 9-701208 

5-24 

10•298792 

’ '9 

42 

652555 

4-18 

961082 

1 -06 

70 i 523 

5-24 

298477 

18 

43 

662806 

4-18 

960968 

1 -06 

701837 

5-24 

29816.3 

! 17 

44 

653 o 87 

4 -18 

o 6 oqo 5 

r -06 

702162 

5-24 

297848 

16 

45 

6533 o 8 

4 • 18 

950841 

1 -06 

702466 

5-24 

297534 

i 5 

46 

653558 

4-17 

960778 

1 -06 

702780 

5-23 

297220 

14 

47 

6538 o 8 

4 -i 1 

950714 

1 -06 

703095 

5-23 

296905 

i 3 

48 

654069 

4-17 

960600 

1 -06 

703409 

5-23 

296591 

12 

49 

654309 

4-16 

95 o 586 

1 -06 

703723 

5-23 

296277 

11 

5 o 

654558 

4-16 

960622 

1-07 

704036 

5-22 

295964 

i 10 

5 i 

9-654808 

4 -16 

9-960458 

1-07 

9 - 7 o 435 o 

5-22 

10-295650 


52 

655 o 58 

4-16 

950394 

1 -07 

704663 

5-22 

296337 


53 

655307 

4-15 

95o33o 

1-07 

704977 

5-22 

296023 

7 

54 

655556 

4-15 

960266 

1.07 

706290 

5-22 

294710 

6 

55 

6558 o 5 

4-15 

960202 

1 -07 

706603 

5-21 

294397 

5 

56 

656 o 54 

4 -i 4 

960138 

1-07 

705916 

5-21 

294084 

! 4 

5 7 

6563 o 2 

4 -14 

960074 

1 -07 

706228 

5-21 

298772 

3 

58 

j 65655 1 

4 - U 

960010 

1-07 

706541 

5-21 

29.3459 

2 

69 

656799 

4 • 1 3 

949945 

1-07 

706864 

5-21 

298146 

1 1 

60 

657047 

4-13 

949881 

1 -07 

707166 

5-20 

292834 

0 


i Cosine 

D. 

Sine 

1 D. 

1 Co tang. 

D. 

fct 

| 

M. 


(G 3 DEGREES.) 



















































































SINES AND TANGENTS. (27 DEGREES.) 45 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

. 

Cotang. 

•n 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

1 5 

16 

*7 

18 

*9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

3? 

31 

32 

33 

34 

35 

36 

37 

38 

3 9 

40 

4 1 

42 

43 

44 

45 

46 

47 

48 

it 

51 

52 

53 

54 

55 

56 

57 

58 
5? 
60 

9-657047 
657295 
657542 
657790 
658o37 
658284 
658531 
658778 
659026 
659271 
659517 

9-659763 
660009 
66o255 
66o5oi 
660746 
660991 
661236 
661481 
661726 
661970 

9-662214 
662469 
662703 
662946 
663190 
663433 
663677 
663920 

664163 

664406 

9•664648 
664891 
665133 
665375 
665617 

666809 
666100 
666342 
666583 
666824 

9•667066 
667306 
667646 
667786 
668027 
668267 
6685o6 
668746 

668986 

669226 

9•669464 
669703 
669942 
670181 
670419 
670668 
670896 
671134 
671372 
671609 

4-13 

4-13 
4-12 

4-12 
4*12 

4-12 

4* 11 

4’ 11 

4-11 

4-10 

4-10 

4-10 
4-09 
4-09 
4-09 

4-09 
4-o8 

4-08 

4-08 
4-07 
4-07 

4-07 

4-07 

4-06 

4" 06 

4* 06 
4-o5 
4-o5 
4-oo 
4-o5 
4 -o 4 

4 • 04 
4-o4 
4*o3 
4*o3 
4-o3 
4’02 
4‘02 

4- 02 
4*02 
4-oi 

4-oi 

4-oi 

4-oi 

4-oo 

4-oo 

4 • 00 

3*99 

3-99 

3-99 

3.99 

3- 9 8 

3 -o 8 

3-98 

D97 

3*97 

3*97 

3*97 

3-96 

3-96 

3-96- 

9-949881 

949816 

949762 

949688 

949623 

949558 

949494 

949429 

949364 

949300 

949235 

9-949170 

949105 

949040 

948975 

948910 

948845 

948780 

948715 

948660 

948584 

9-948519 

948454 

948388 

948323 

948257 

948192 

948126 

948060 

947995 

947929 

9-947863 

947797 
947731 
047666 
947600 
947533 
947467 
947401 

947335 

947269 

9-947203 

947136 

947070 

947004 

946937 

946871 

946804 

946738 

946671 

946604 

9-946538 

946471 

946404 

946337 
946270 
946203 
946136 
946069 
946002 
945935 

1-07 

1-07 

1-07 

1 -08 

1 -08 

1 -08 

1 -08 

1 -08 

1 -08 

1 -08 

1 -08 

1 -08 

1 -o3 

1 -08 
i-08 

1 -08 

1 -08 

1 -09 

1 -09 

1 -09 

1 -09 

1 -09 

1 -09 

1 -09 

1 -09 

1 -09 
1-09 

1 -09 

1 -09 

1 • 10 

1 • 10 

1 • 10 

l-IO 

1 • 10 

1 • 10 

1 • 10 

1 • 10 

1 • 10 

1 • 10 

1-10 

I • 10 

I • 10 

I • 11 

I • 11 

I • 11 

I • 11 

I • 11 

I • 11 

I • 11 

1-11 

1 • 11 

I • 11 

I ■ 11 

I • 1 1 

I • 11 

1-12 

1-12 

1-12 

1-12 

I • 12 

1-12 

9-707166 

707478 

707790 

70S102 

708414 

708726 

709037 

709349 

709660 

709971 

710282 

9-710593 

7i0904 
711215 

711525 

711836 
712146 

712456 

712766 

713076 

713 3 86 

9.713696 

714006 

714314 

714624 

714933 

716242 

715551 
716860 
716168 

7 l6 477 

9.716785 

717093 

717401 

717709 

718017 

718325 

718633 

718940 

719248 

719555 

9.719862 

720169 

720476 

720783 

721089 
721396 
721702 
722009 
722315 
722621 

9-722927 

723232 

723538 

723844 

724149 

724454 

724709 

720060 

725369 

726674 

5-20 

5-20 

5-20 

5-20 

5*19 
5-19 
5-19 
5-19 
5-19 

5 -18 
5-i8 

5-i8 
5-i8 
5-18 
5.17 
5-17 
5-17 
5-17 
5-i6 
5-16 
5-i6 

5-16 
5-16 
5-io 

5 • 15 
5-15 
5-15 
5-14 
5- U 
5-14 
5-i4 

5 -14 
5-13 

5 • 1 3 
5-13 

5 -13 

5 -13 
5-12 
5-12 
5-12 
5-12 

5-12 
5-11 
5-n 

5-11 
5-i 1 

5-11 

5-10 
5-io 
5-io 
5-10 

5- io 

6- 09 
6-09 
6-09 
5-09 
5-09 
5-08 
5-o8 
5-oS 
5-08 

io-292834 
292622 
292210 
291898 
291586 
291274 
290963 
290661 
290340 
290029 
289718 

10-289407 

289096 

288785 

288475 

288164 

287864 

287544 

287234 

286924 

286614 

io- 2863 o 4 

285995 

286686 

280376 

286067 

284758 

284449 

284140 

283832 

283523 

io-283215 
282907 
282699 
282291 
281983 
281670 
281367 
281060 
280702 
280445 

io- 28 oi 38 
279831 
279624 
279217 
278911 
278.604 
278298 
277991 
277686 
277379 

10-277073 

276768 

276462 

276106 

270801 

275046 

270241 

274935 

274631 

274326 

60 

5o 

58 

57 

56 

50 

04 

53 

52 

51 

5o 

49 

48 

47 

46 

45 

44 

43 

42 

4i 

40 

39 

38 

37 

36 

35 

34 

33 

32 

3i 

3o 

20 

28 

27 

26 

25 

24 

23 

22 

21 

20 

I? 

l8 

17 

l6 

i5 

14 

i3 

12 

11 

JO 

7 

6 

5 

4 

3 

2 

1 

0 

_ 

Cosine 

D. 

Sine 

D. 1 Cotang. 

D. 

Tang. 

M. 


(G2 DEGREES.) 































































(28 DEGREES.) A TABLE OF LOGARITHMIC 


46 


M. 

Sine 

D. 

Cosine 

D. 

Tung. 

D. 

Cotang. | 

I 


0 

9-671609 

3-96 

3-96 

3-96 

3-95 

3-95 

9 ' 945 o 35 

1 • 12 

9-725674 

5 08 

10-274326 i 

60 

1 

2 

671847 

672084 

946868 

945800 

1 • 12 

1 • 12 

725979 

726284 

5 08 
5-07 

274021 1 
273716 | 

5? 

57 

3 

672321 

672558 

945733 

1-12 

726688 

5-07 

273412 i 

4 

945666 

I • 12 

726892 

5 -o? 

273108 ; 

56 

5 

672796 

3-94 

945598 

I • 12 

727197 

5- 07 

6- 07 

5 -06 

5 -06 

5 -06 

272803 ; 

55 

6 

l 

q 

673032 

673268 

6735 o 5 

673741 

3-94 

3-94 

3-94 

3-93 

94553 i 

946464 

945396 

945323 

1-12 
i • 1 3 

1 • 1 3 

1 • i 3 

727601 

727805 

728109 

728412 

272499 | 
272195 
27189I 
271588 

54 

53 

52 

5 i 

10 

673977 

3-93 

945261 

1 • i 3 

728716 

5 -06 

271284 

5 o 

11 

9 674213 

3-93 

9-945198 

1 • i 3 

9-729020 

5 - 06 

I0-27098C 

49 

12 

674448 

3-92 

945125 

1 • i 3 

729323 

5 -o 5 

27O677 

48 

i 3 

674684 

3-92 

945 o 58 

1 • 1 3 i 

729626 

5 -o 5 

270374 

47 

14 

674919 

3-92 

94499 ° 

1 • 1 3 

729929 

5 -o 5 

27007I 

46 

i 5 

675 i 55 

3-92 

944922 

1 • 1 3 

730233 

5 -o 5 

269767 

45 

16 

675390 

3-91 

944854 

1 * 1 3 

73o535 

5 -o 5 

269466 

44 

17 

676624 

676859 

3-91 

944786 

1 • i 3 

73 o 838 

5 -o 4 

269162 

43 

18 

3 -gi 

944718 

1 • i 3 

73 ii 4 i 

6-04- 

268859 

42 

19 

676094 

3-91 

94465 o 

1 • 1 3 

73 i 44 'i 

5 -o 4 

268556 

41 

20 

676828 

3-90 

944582 

1 • 14 

731746 

5 -o 4 

268264 

40 

21 

9-676662 

3-90 

9 - 9445 i 4 

1 • 14 

9-732048 

5 -o 4 

10-267952 

39 

22 

676-796 

3-90 

944446 

1 -14 

73235 1 

5 -o 3 

267649 

38 

23 

677030 

3-90 

944377 

1 • U 

732653 

5 -o 3 

267347 

37 

24 

677264 

8-89 

944309 

1 • 14 

732955 

5 -o 3 

267046 

36 

25 

677498 

3-89 

944241 

1 • 14 

733257 

5 -o 3 

266743 

35 

26 

677781 

3 - 8 9 

94417 2 

1 • 14 

733558 

5 -o 3 

266442 

34 

27 

677964 

3-88 

944104 

1 • 14 

73386 o 

5-02 

266140 

33 

28 

678197 

3-88 

944086 

1-14 

734162 

5-02 

265838 

32 

29 

678430 

3-83 

943967 

1 • 14 

734463 

5-02 

265537 

3 i 

3 o 

678663 

3-83 

948899 

i-14 

734764 

5-02 

265236 

3 o 

3 i 

9-678895 

3-87 

9 - 94383 o 

1 • 14 

9 - 735 o 66 

5-02 

10-264934 

29 

32 

679128 

3-87 

943761 

1 • 14 

735367 

5-02 

264633 

28 

33 

679360 

3-87 

3-87 

943693 

1 -1 5 

735668 

5 -oi 

264332 

27 

34 

679692 

943624 

1 * 1 5 

735969 

5 -oi 

264031 
263731 

26 

35 

679824 

68 oo 56 

3-86 

943555 

1 • i 5 

736269 

5 -oi 

25 

36 

3-86 

943486 

1 • 1 5 

736670 

5 -oi 

26343 0 

24 

'll 

680288 

680619 

3-86 

3-85 

943417 

943348 

1 • 1 5 

1 -1 5 

736871 

737171 

5 -oi 

5 -oo 

263 129 
262829 

23 

22 

3 g 

680760 

3-85 

943279 

1 • i 5 

737471 

5 -oo 

262529 

21 

40 

680982 

3-85 

943210 

1 * 1 5 

737771 

5 -oo 

262229 

20 

4 i 

9-68121 3 

3-85 

9- 943 i 4 i 

1 * 1 5 

9-738071 

5 -oo 

10-261929 

19 

42 

68 i 443 

3 - 84 ' 

943072 

1 • i 5 

7383 7 1 

5 -oo 

261629 

l8 

43 

681674 

3-84 

943 oo 3 

1 • 1 5 

738671 

4-99 

261329 

17 

44 

68 igo 5 

3-84 

942934 

1 • 1 5 

738971 

4-99 

261029 

16 

45 

682 i 35 

3-84 

942864 

1 • i 5 

739271 

4-99 

260729 

i 5 

46 

682365 

3-83 

942795 

1 • 16 

739670 

4-99 

260430 

14 

47 

682095 

3-83 

942726 

1 • 16 

739870 

4-99 

26 oi 3 o 

i 3 

48 

882825 

3-83 

942656 

942587 

1 *16 

740169 

4-99 

259831 

12 

49 

683 o 55 

3-83 

1 • 16 

740468 

4-98 

259532 

1 11 

DO 

683284 

3-82 

942517 

1 • 16 

740767 

4-98 

259»33 

10 

5 i 

9 - 683 5 14 

3-82 

9-942448 

1 • 16 

9-741066 

4-98 

10-258934 

0 

52 

683 7 43 

t 3-82 

942378 

1 • 16 

741 365 

4-98 

258635 

8 

53 

683972 

| 3-82 

942808 

1 • 16 

741664 

4-98 

258336 

7 

5-4 

684201 

3 -81 

942239 

1 • 16 

741962 

4-97 

258 o 38 

6 

55 

6 S 443 o 

3 -81 

942169 

1 • 16 

742261 

4-97 

267739 

5 

56 

684658 
i 684887 

I 3 -81 

942099 

1 • 16 

742559 

4-97 

257441 

4 

67 

3 -So 

942029 

j 1 • 16 

742858 

4-97 

267142 

1 ^ 

58 

I 685 ii 5 

3 -80 

941969 

941089 

1 • 16 

743 1 56 

4-97 

256844 

2 

59 

| 685343 

3 -80 

1-17 

743454 

1 4-97 

256546 

I 

60 

685571 

! 3 -80 

, 941819 

1 • 17 

743752 

j 4-96 

266248 

0 

1 


Cosine 

1). 

sine 

D. 

Cotang. 

! D. 

Tang. 

1 Mi, 


(6 L DEGREES.) 



































































SINES AND TANGENTS. (29 DEGREES.) 47 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

j Cotang. 

1- 

o 

9-685571 

j 3-80 

9-941819 

1-17 

9-743752 

4-96 

10-256248 

60 

i 

680799 

3-79 

941749 

1 * 17 

744 o 5 o 

4-96 

266900 

5 q 

2 

686027 

3-79 

941679 

i-n 

744348 

4-96 

200652 

58 

3 

686254 

3-79 

941609 

1 * 17 

744645 

4-96 

255355 

! _ 

37 

4 

686482 

3-79 

94i53g 

1 * 17 

744943 

4.96 

255 o 57 

56 

D 

686709 

3-78 

941469 

1-17 

745240 

4-96 

204760 

55 

6 

686936 

3-78 

94i3g8 

i-i 7 

745538 

4-90 

254462 

54 

2 

687163 

3 • 78 

94 i 328 

1 • 17 

745835 

4-95 

254i65 

53 

8 

687389 

3 • 78 

941258 

i-i 7 

746132 

4-96 

253868 

52 

9 

687616 

3.77 

941187 

1 ' 1 7 

746429 

4-90 

253571 

5j 

10 

007843 

3-77 

941117 

1-17 

746726 

4-90 

253274 

5o 

ii 

9-688069 

3-77 

9-941046 

1 • 18 

9-747023 

4-94 

10-252977 

49 

I 2 

68829D 

3-77 

940975 

1 • 18 

747319 

4.94 

262681 

48 

i3 

688521 

3-76 

940906 

1 • 18 

747616 

4-94 

252384 

47 

14 

688747 

3-76 


1 • 18 

7479 1 3 

4-94 

252087 

46 

ID 

688972 

3-76 

940763 

1 • 18 

748209 

4.94 

251791 

45 

io 

689198 

3-76 

940693 

1 • 18 

7485 o 5 

4.93 

201495 

44 

17 

689423 

3-75 

940622 

1 • 18 

748801 

4-98 

251199 

43 

IO 

689648 

3-75 

940551 

1 • 18 

749097 

4.93 

25ogo3 

42 

*9 

689873 

3-75 

940480 

1 * 18 

7493 o 3 

4-98 

260607 

4i 

20 

690098 

3 - 75 

940409 

1*18 

749689 

4-98 

25 o 3 ii 

4o 

21 

9-690323 

3-74 

9-940333 

1 • 18 

9-749985 

4-98 

io- 25 ooi 5 

3 9 

22 

690548 

3-74 

940267 

1 • 18 

750281 

4-92 

249719 

38 

23 

690772 

3-74 

940196 

1 • 18 

700576 

4-92 

249424 

37 

24 

690996 

3-74 

940125 

1-19 

700872 

4-92 

249128 

36 

25 

691220 

3-73 

940054 

1-19 

701167 

4-92 

248833 

35 

20 

691444 

3-73 

939982 

1-19 

701462 

4-92 

248538 

34 

27 

691668 

3-73 

939911 

1-19 

701757 

4-92 

248243 

33- 

28 

691892 

3-73 

939840 

i-i 9 

762052 

4-9 1 

247948 

32 

29 

692115 

3-72 

989768 

i-i 9 

702347 

4-9 1 

247653 

3i 

3o 

692339 

3-72 

939697 

1-19 

762642 

4-9 1 

247358 

3o 

3i 

9-692562 

3*72 

9-939625 

1*19 

9-702937 

4.91 

10-247063 

29 

32 

692785 

3-71 

939554 

1-19 

753231 

4.91 

246769 

28 

33 

693008 

3*71 

939482 

1-19 

753526 

4-91 

246474 

27 

34 

693231 

3.71 

939410 

1 * 19 

753820 

4.90 

246180 

26 

35 

693453 

3*71 

989339 

1-19 

754 ii 5 

4.90 

246886 

25 

36 

693676 

3-70 

939267 

1 • 20 

704409 

4.90 

245591 

24 

37 

693898 

3-70 

939195 

1 • 20 

754706 

4.90 

246297 

23 

38 

694120 

3-70 

939123 

1 • 20 

754997 

4.90 

246008 

22 

1 OQ 

694342 

3-70 

939052 

1 • 20 

755291 

4.90 

244709 

21 

1 40 

694664 

3-69 

936980 

1 • 20 

755585 | 

4.89 

244410 

20 

4i 

9•694786 

3-69 

9-938908 ; 

1-20 

9-765878 J 

4.89 

10-244122 

IO 

42 

696007 


9 38836 

1-20 

766172 

4.89 

243828 

l8 

43 

696229 

3-6 q 

988763 

I -20 

766465 

4.89 

243535 

17 

44 

696450 

3-68 

938691 

I -20 

766769 

4.89 

243241 

l6 

45 

696671 

3-68 

938619 

1-20 

707062 

4.89 

242948 

i5 

46 

695892 

3-68 

938547 

I -20 

707345 

4-88 

242655 

14 

47 

696113 

3-68 

938476 

I -20 

757638 

4-88 

242862 

i3 

48 

696334 

3-67 

938402 

I • 21 

707931 

4-88 

242069 

12 

49 

696554 

3-67 

g3833o 

I -21 

768224 

4.88 

241776 

11 

5o 

69677D 

3-6 7 

938258 

I -21 

758617 

4-88 

241483 

10 

5i 

9-696995 

3-67 

9-938185 

I -21 

9-768810 

4.88 

10-241190 

9 

52 

697216 

3-66 

988113 

I -21 

759102 

4.87 

240898 

8 

53 

697435 

3-66 

938040 

I -21 

769895 

4-87 

24 o 6 o 5 

7 

54 

697664 

3-66 

937967 

I • 21 

759687 

4.87 

24 o 313 

6 

55 

697874 

3-66 

937896 

I -21 

709979 

4-87 

240021 

5 

56 

698094 

3-65 

937822 

I -21 

760272 

4-87 

239728 

4 

37 

698813 

3-65 

937749 

1-21 

760564 

4-87 

239436 

3 

58 

698532 

3-65 

987676 

I • 21 

760806 

4-86 

239144 

2 

69 

698761 

3-65 

937604 

I -21 

761148 

4-86 

238852 

1 

60 

698970 

3*64 

937531 

I -21 

761439 

4-86 

23856 i 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M._ 


27 


(60 DEGREES.) 
























































































48 


(30 DEGREES.) A TABLE OF LOGARITHMIC 


M. i 

Sine 

0 

1 

9-698970 
699189 

2 

699407 

3 

699626 

4 

699844 

5 

700062 

6 

700280 

7 

700498 

8 

700716 

9 

700933 

10 

7011 5 1 

11 

9-701368 

12 

7 oi 585 

i 3 

701802 

U 

702019 

i 5 

702236 

16 

702452 

ll 

702669 

702886 

l 9 

7 o 3 ioi 

20 

703317 

21 

9-703533 

22 

703749 

23 

703964 

24 

704*79 

25 

704396 

26 

704610 

27 

704826 

28 

705040 

29 

705254 

3 o 

706469 

3 i 

9 * 7 o 5683 

32 

70589S 

33 

706112 

34 

706326 

35 

706539 ' 

36 

706758 | 

37 

706967 

38 

707180 

3 9 

707393 

4 o 

707606 j 

4 i 

9-707819 

42 

7 o 8 o 32 

43 

708245 

44 

708458 

43 

708670 

46 

708882 

47 

709094 

48 

709306 j 

49 

709518 1 

5 o 

70973 o | 

5 i 

9-709941 

52 

7ioi53 | 

53 

7 io 364 

34 

710675 

55 

710786 

5 b 

710997 

57 

711208 

58 

711419 

5 9 

711629 

60 

7 ii 83 9 


Cosine 


D. 


3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

o 

O 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 


64 

64 

64 

64 

63 

63 

63 

63 

63 

62 

62 

62 

62 

61 

61 

61 

61 

60 

60 

60 

60 

r 9 

Si 

58 

58 

58 

57 

5 7 

57 

57 

56 

56 

56 

56 

55 

55 

55 

55 

54 

54 

54 

54 

53 

53 

53 

53 

53 


52 
52 
52 
52 

5i 
5i 

5i 
5i 
5o 
3-5o 


Cosine 


D. 


9-937531 

937458 

937385 

937312 

937238 

937166 

937092 

937019 

936946 

936872 

936799 

9-936725 

936652 

936578 

9365o5 

93643i 

936357 

936284 
936210 
9361 36 
936062 

9-935988 

935914 

935840 

935766 

935692 

935618 

935543 

935469 

935390 

935320 

9-935246 

935171 

930097 

935022 

934948 

934873 

934798 

934723 

934649 

934674 

9-934499 

934424 

934349 

934274 

934«99 

934*28 

934048 

933973 

933898 

933822 

9-933747 

933671 

933596 

933520 

933445 

93336o 

933290 

933217 

933i4i 

o33o66 


Sine 


D. 

Tang. 

D. 

Cotang. 


I -21 

9-761489 

4-86 

io-238561 

60 

I -22 

761731 

4-86 

288269 

59 

1-22 

762023 

4 • 86 

287977 

58 

1-22 

762314 

4-86 

237666 

57 

I -22 

762606 

4-85 

237394 

56 

I -22 

762897 

4-85 

237103 

55 

I -22 

763188 

4-85 

236812 

54 

1-22 

7634-9 

4-85 

236521 

53 

I -22 

763770 

4-85 

23623o 

52 

1-22 

1-22 

764061 

764362 

4-85 

4-84 

230939 

235648 

61 

5 o 

1-22 

9•764643 

4-84 

10-235357 

49 

1-23 

764933 

4-84 

236067 

48 

1-23 

766224 

4-84 

234776 

47 

1-23 

766614 

4-84 

234486 

46 

1-23 

766806 

4-84 

234196 

45 

I - 23 

766095 

4-84 

233905 

44 

I -23 

766385 

4-83 

2336 i 5 

43 

1-23 

766675 

4-83 

233325 

42 

1-23 

766965 

4-83 

233 o 35 

41 

1-23 

767235 

4-83 

232745 

40 

1-23 

9-767545 

4-83 

10-232455 

3 9 

1-23 

767834 

4-83 

232166 

38 

1-23 

768124 

4-82 

231876 

37 

1-24 

768413 

4-32 

231687 

36 

1-24 

768703 

4-82 

23 1297 

35 

1-24 

768992 

4-82 

231008 

34 

1-24 

769281 

4-82 

280719 

33 

1-24 

769670 

4-82 

23 o 43 o 

32 

1-24 

769860 

4-8i 

23 oi 4 o 

3 i 

1-24 

770148 

4 * B1 

229852 

3 o 

1-24 

9.770437 

4-8i 

10-229563 

20 

1-24 

770726 

4 * B1 

229274 

28 

1-24 

771015 

4 • 81 

228985 

2 7 

1-24 

77i 3 o 3 

4-8i 

228697 

26 

1-24 

771092 

4*81 

2284Q8 

26 

1-24 

771880 

4-80 

228120 

24 

I • 25 

772168 

4 - 8 o 

227832 

23 

I -25 

772457 

4-So 

227643 

22 

I -25 

77 2 745 

4 -80 

227255 

21 

I • 25 

773o33 

4-8o 

226967 

20 

I • 25 

9-773321 

4-8o 

*0-226679 

10 

1-25 

773608 

4-79 

226392 

18 

1-25 

778806 

4-79 

226104 

*7 

1-25 

774134 

4-79 

226816 

16 

1-25 

77447 1 

4-79 

225529 

i 5 

1-25 

774739 

4-79 

225241 

14 

1-25 

776046 

4-79 

224964 

1 3 

1-25 

775333 

4-79 

224667 

12 

I -26 

775621 

4-78 

224379 

11 

I • 26 

776908 

4-78 

224092 

10 

1.26 

9-776195 

4-78 

*o- 2238 o 5 

9 

1 1-26 

776482 

4-78 

2235 i 8 

8 

I • 26 

776769 

4-78 

22323 I 

7 

1-26 

777050 

4-78 

222945 

6 

I • 26 

777342 

4-78 

222658 

1 5 

I • 26 

777628 

j 4-77 

222372 

4 

I -26 

777915 

4-77 

222085 

3 

I • 26 

778201 

4-77 

221799 

2 

I -26 

778487 

4-77 

221612 

1 1 

1 -26 

773774 

! 4-77 

221226 

0 

D. 

Cotang. 

D. 

Tang. 



(59 DEGREES.) 



































































SINES AND TANGENTS. (31 DEGREES.) 


49 


1 H. 

Sino 

D. 

Cosine 

D. 

0 

9-711839 

3 - 5 o 

9-933066 

1 • 26 

1 

2 

3 

7I2o5o 

712260 

712469 

3 - 5 o 

3 - 5 o 

3-49 

932990 

932914 

9 32838 

1 • 27 
1-27 
1 -27 

4 

712679 

3-49 

932762 

1 *27 

5 

712889 

3-49 

932685 

1-27 

6 

713098 

3-49 

932609 

1-27 

7 

7i33o8 

3-49 

932533 

1 - 27 

8 

713517 

3-48 

932467 

1 • 27 

9 

713726 

3-48 

93238o 

1 -27 

io 

713935 

3-48 

9323 o 4 

1 • 27 

11 

9 - 7 I 4 I 44 

3-48 

9-982228 

1 -27 

12 

714352 

3-47 

93 21 5 1 

1-27 

i 3 

714361 

3-47 

932075 

931998 

1 -28 

i 4 

714769 

3-47 

1 -28 

i 5 

714978 

3-47 

931921 

1-28 

16 

71 5 186 

3-47 

931845 

1-28 

n 

715394 

3-46 

931768 

I -28 

18 

716602 

3-46 

931691 

1-28 

19 

716809 

3-46 

981614 

1-28 

20 

716017 

3-46 

931 537 

I • 28 

21 

9-716224 

3-45 

9-931460 

1-28 

22 

716432 

3-45 

981883 

1-28 

23 

716639 

3-45 

93i3o6 

1-28 

24 

716846 

3 -45 

981229 

I -29 

23 

717063 

3-45 

93 I 1 52 

I • 29 

26 

717259 

3 -44 

981075 

I -29 

27 

717466 

3-44 

930998 

I -29 

28 

29 

717673 

717879 

3-44 

3 • 44 

930921 

980843 

I • 29 

1-29 

3 o 

718085 

3-43 

980766 

I -29 

3 i 

9-718291 

3-43 

9-980688 

1-29 

32 

718497 

3-43 

93061I 

1-29 

33 

718703 

3-43 

93o533 

1-29 

34 

718909 

3-43 

93o456 

I -29 

35 

719114 

3 -42 

980378 

I -29 

35 

719320 

3-42 

93o3oo 

1 - 3 o 

37 

719525 

3-42 

980228 

1 - 3 o 

38 

719730 

3-42 

93oi45 

1 - 3 o 

3 9 

719935 

3 - 41 

930067 

1 - 3 o 

4 o 

720140 

3 • 41 

929989 

1 - 3 o 

4 i 

9-720345 

3 - 4 1 

9-929911 

1 -3o 

42 

720549 

• 3 - 4 i 

929833 

1 -3o 

43 

720754 

3 - 4 o 

929755 

1 -3o 

44 

720958 

3 - 4 o 

929677 

1 -3o 

45 

721162 

3 -40 

929699 

1 - 3 o 

46 ■ 

72 i 366 

3 - 4 o 

929621 

1 - 3 o 

47 

721670 

3 - 4 o 

929442 

1 - 3 o 

48 

721774 

3-39 

929864 

i - 3 r 

4 ? 

721978 

3 - 3 9 1 

929286 

i - 3 1 

DO ! 

1 

722181 

3-39 j 

929207 

1 • 3 1 

5 i 

9-722385 

3 - 3 9 

9-929129 

1 - 31 

52 

722688 

3 - 3 o 

920060 

928972 

1 - 3 1 

53 

722791 

3-38 

1 • 3 1 

54 

722994 

3-38 I 

928898 

1 - 3 i 

55 

723197 

3-38 

928816 

1 * 3 i 

56 ' 

723400 

3-38 

928736 

1 - 3 i 

5- 

7236o3 

3-37 

928667 

r • 3 1 

58 

7238 o 5 

3 - 3 ~i 

928678 

1 - 3 i 

5 9 

724007 

3-37 

928499 

1 - 3 i 

60 

724210 

3 - 3 7 

928420 

1 • 3 1 


Cosine 

D. 

Siue 

D. 


1 Tang. 

i 0 

D. 

Cotang. 

0 


9-778774 

4-77 

10-221226 

60 

779060 

4-77 

220940 

69 

779346 

4-76 

220654 

58 

779682 

4-76 

22o368 

5 7 

779918 

4-76 

220082 

56 

780203 

4-76 

219797 

55 

780489 

4-76 

219511 

54 

780775 

4-76 

219225 

53 

781060 

4-76 

218940 

52 

781346 

4-76 

218654 

5i 

781631 

4-75 

218369 

5o 

9-781916 

4-75 

10-218084 

49 

j 782201 

4-75 

217799 

48 

782486 

4-75 

2I75l4 

47 

782771 

4-75 

217229 

46 

783o56 

4-75 

216944 

45 

783341 

4-75 

2l6659 

44 

783626 

4-74 

216374 

216090 

43 

783910 

4-74 

42 

784195 

4-74 

2 i 58 o 5 

41 

784479 

4-74 

2 i 55 pi 

40 

9-784764 

4-74 

io-21 5236 

39 

786048 

4-74 

214952 

38 

785332 

4-73 

214668 

37 

7856 i 6 

4-73 

214384 

36 

786900 

4-73 

214100 

35 

786184 

4-73 

213816 

34 

786468 

4-73 

21353 2 

33 

786752 

4-73 

213248 

32 

787036 

4-73 

212964 

3i 

787319 

4-72 

212681 

3o 

9-787603 

4-72 

10-212397 

29 

787886 

4-72 

212114 

28 

788170 

4-72 

21i83o 

27 

788453 

4-72 

211547 

26 

788736 

4-72 

211264 

25 

789019 

4-72 

210981 

24 

789302 

4-71 

210698 

23 

789585 

4-71 

210415 

22 

789868 

4-71 

210132 

21 

790151 

4-71 

209849 

20 

9-790433 

4-71 

10-209567 

19 

790716 

4-71 

209284 

IO 

790999 

791281 

4-71 

209001 

17 

4-71 

208719 

l6 

791563 

4-70 

208437 

i5 

791846 

4-70 

208154 

14 

792128 

4-70 

207872 

i3 

792410 

4-70 

207690 

12 

792692 

4-70 

.207308 

11 

79 2 974 

4-70 

207026 

10 

9*793256 
793538 
793S19 

4-70 

4-69 

4-69 

10-206744 

206462 

206181 

7 

794101 

4-69 

205899 

6 

794383 

4-69 

2o56i7 

5 

794664 

4-69 

205336 

4 

794945 

4-69 

2 o 5 o 55 

3 

795227 

4-6 9 

204773 

2 

7955o8 

4-68 

204492 

1 

796789 

4-68 

204211 

c 

Cotang. i 

D. 

Tang. 

M. 


(58 DEGREES.) 


































































50 


(32 DEGREES.) A TABLE OF LOGARITHMIC 


Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


o 

9-724210 

3-37 

9-928420 

i 

724412 

3-37 

928342 

2 

724614 

3-36 

928263 

3 

724816 

3-36 

928183 

4 

726017 

3-36 

928104 

5 

725219 

3-36 

928026 

6 

725420 

3-35 

927946 


725622 

3-35 

927867 

9 

726823 

726024 

3-35 

3-35 

927787 

927708 

10 

726226 

3-30 

927629 

11 

9-726426 

3-34 

9 - 927 5 49 

92747° 

12 

726626 

3-34 

i 3 

726827 

3-34 

927390 

U 

727027 

3-34 

927310 

i 5 

727228 

3-34 

927231 

16 

727428 

3-33 

927161 

17 

727628 

3-33 

927071 

ib 

727828 

3-33 

926991 

19 

728027 

3-33 

926911 

20 

728227 

3-33 

926831 

21 

9-728427 

3-32 

9-926751 

22 

728626 

3-32 

926671 

23 

728825 

3-32 

926591 

24 

729024 

3-32 

92651 X 

20 

729223 

3 * 3 1 

926431 

26 

729422 

3 - 3 1 

92635 i 

27 

729621 

3 - 3 1 

926270 

28 

729820 

3 • 3 1 

926190 

29 

730018 

3 - 3 o 

926110 

3 o 

730216 

3 - 3 o 

926029 

3 r 

9-73041 5 

3 - 3 o 

9-926949 

920868 

32 

73 o 6 1 3 

3 - 3 o 

33 

73 o 8 i1 

3 - 3 o 

920788 

34 

731009 

3-29 

925707 

35 

731206 

3 • 29 

925626 

36 

781404 

3-29 

925545 

37 

73 i 6 o 2 

3-29 

925465 

38 

731799 

3-29 

925384 

39 

731996 

3-28 

9253o3 

4 o 

732193 

3-28 

925222 

4 i 

9-732390 

3-28 

9-925141 

42 

732687 

3-28 

925o6o 

43 

782784 

3-28 

924079 

44 

732980 

3-27 

924897 

40 

733177 

3-27 

924816 

46 

733373 

3-27 

924735 

47 

48 

733569 

733765 

3-27 

3-27 

924654 

924672 

49 

733961 

3 • 26 

92449 1 

5 o 

734 i 57 

3-26 

924409 

5 i 

9-734353 

3-26 

9-924328 

52 

734549 

3 • 26 

924246 

53 

734744 

3-25 

924164 

54 

734 q 39 

3-25 

924083 

00 

735 1 35 

3-25 

924001 

56 

73533 o 

3-25 

923919 

57 

735525 

3-20 

923837 

58 

735719 

3-24 

923755 

59 

786914 

3-24 

9236-3 

60 

786109 

3-24 

923091 

1_ 

• 

1 Cosine 

D. 

1 Sine 


(57 


I -32 

9.790789 

4-68 

10-204211 

60 

1-32 < 

796070 

4-68 

2 o 3 g 3 o 

°9 

1-32 

796351 

4-68 

203649 

58 

1-32 

796632 

4-68 

203368 

57 

1-32 

796913 

4-68 

203087 

56 

1-32 

797*94 

4-68 

202806 

55 

I -32 

79747 ° 

4-68 

202525 

54 

1-32 

797755 

4-68 

202245 

53 

I -32 

798036 

4-67 

201964 

52 

1-32 

798316 

4-67 

201684 

5i 

I -32 

798696 

4-67 

201404 

5o 

I -32 

9-798877 

4-67 

10-201123 

49 

1-33 

799167 

4 - 67 

200843 

48 

i -33 

799437 

4-67 

2 oo 563 

47 

i -33 

799717 

4-67 

200283 

46 

i -33 

799997 

4-66 

200003 

45 

i -33 

800277 

4-66 

199723 

44 

i -33 

800067 

4-66 

199443 

43 

i -33 

8 ooS 36 

4-66 

190164 

42 

i -33 

801116 

4-66 

198884 

41 

i -33 

801396 

4-66 

198604 

40 

i -33 

9-801675 

4-66 

10-198326 

3g 

i -33 

801960 

4-66 

198045 

38 

i -33 

802234 

4-65 

197766 

37 

i -34 

802613 

4-65 

197487 

36 

1 -34 

802792 

4-65 

197208 

35 

i -34 

808072 

4-65 

196928 

34 

1 • 34 

8o335i 

4-65 

196649 

33 

1 -34 

8 o 363 o 

4-65 

196370 

32 

1 -34 

8 o 3 go 8 

4-65 

196092 

31 

x -34 

804187 

4-65 

196813 

3o 

I-n 4 

9•804466 

4-64 

10-195534 

29 

i- J 4 

8 o 4745 

4-64 

195255 

28 

1 -34 

8o5o23 

4-64 

194977 

2 7 

1 -34 

8o53o2 

4-64 

I94698 

26 

1 -34 

8 o 558 o 

4-64 

194420 

25 

1 -35 

806869 

4-64 

194141 

24 

i -35 

806137 

4-64 

iq3863 

23 

1 -35 

80641 5 

4-63 

ig 3585 

22 

1 -35 

806693 

4-63 

193307 

21 

1 - 3 o 

806971 

4-63 

193029 

20 

1-35 

9-807249 

4-63 

io-192761 

1 0 

i -35 

807627 

4-63 

192473 

IO 

1 -35 

807800 

4-63 

192195 

*7 

i -35 

8 o 8 o 83 

4-63 

1919*7 

l6 

1 -35 

8 o 836 i 

4-63 

191639 

i5 

i -36 

8 o 863 S 

4-62 

igi 362 

14 

i -36 

808916 

4-62 

191084 

i3 

i -36 

809193 

4-62 

190807 

12 

i -36 

809471 

4-62 

190629 

11 

i -36 

809748 

4-62 

190262 

10 

i -36 

9-810025 

4-62 

io-189975 

9 

1 -36 

8 io 3 o 2 

4-62 

189698 

8 

i -36 

8io58o 

4-62 

189420 

1 

i -36 

810857 

4-62 

189143 

6 

i -36 

8111 34 

4-6i 

188866 

5 

i -36 

811410 

4-6i 

i 885 go 

4 

i -36 

811687 

4*61 

1 883 1 3 

3 

1-37 

811964 

4-6i * 

i 88 o 36 

2 

1-37 

812241 

4-6i 

187769 

1 

1-37 

812617 

4-6i 

187483 

0 

D. 

Cotang. 

! D. 

Tang. 

M. 


DEGREES,) 











































































SINES AND TANGENTS. (33 DEGREES.) 


51 


M. 

Sine 

D. | 

I 

Cosine 

D. , 

Tang, j 

D. ; 

Cotang. | 

0 

9-736109 

3-24 j 

9-923691 

1-37 j 

9-812517 

4-6i 

10-187482 j 

60 | 

i ! 

7363 o! 

3-24 

923609 

1-37 1 

812794 1 

4-6i 

187206 1 

5 9 

2 ' 

736498 

3-24 

923427 

1-37 

813070 j 

4-6i 

186980 ' 

58 

3 ! 

736692 

3-23 

923345 

i- 3 7 

8 i 3347 1 

4-6c 

186653 | 

57 

4 ! 

736886 

3-23 

923263 

i- 3 7 

8 i 3623 

4-6c • 

186377 1 

C/6 

5 ; 

737080 

3-23 

923181 

i- 3 7 

813899 

4-60 

186101 

55 ' 

6 

737274 

3-23 

928098 

1.37 

814175 

4-6c 

185825 

54 

’ 7 

737467 

3-23 

923016 

1.37 

814462 

4-60 

180048 j 

53 

8 

737661 

3-22 

922933 

i- 3 7 

814728 

4-60 

185272 j 

52 

9 i 

737855 

3-22 

922851 

1 -37 

81 5 oo 4 

4-6o 

184996 . 

5 i 

10 | 

738048 

3-22 

922768 

1 -38 

816279 

4- 60 

184721 

5 o 

11 ! 

9-738241 

3-22 

9-922686 

i -38 

9•81 5555 

4*59 

10-184446 

49 

12 

738434 

3-22 

922603 

1 -^38 

8 i 583 i 

4-59 

184169 

48 

i 3 

738627 

8-21 

922620 

i -38 

816107 

4 - 5 q 

183893 

47 

i 4 

738820 

3-21 

922433 

i -38 

8 i 6382 

4-69 

1 836 18 

46 

i 5 

739013 

3-21 

922355 

i -38 

8 i 6658 

4-59 

183342 

40 

16 

739206 

3-21 

922272 

i -38 

816933 

4.59 

183067 

44 

17 

739398 

3-21 

922189 

i -38 

817209 

4.59 

182791 

43 

18 

739690 

3 • 20 

922106 

i -38 

817484 

4.59 

182016 

42 

10 

739783 

3-20 

922023 

i -38 

817759 

4 - 5 q 

182241 

4 1 

20 

739975 

3 • 20 

921940 

i -38 

8 i 8 o 3 o 

4-08 

181965 

4 o 

21 

9-740167 

3-20 

9-921867 

1-39 

9 - 8 i 83 io 

4-58 

io-181690 

3 9 

22 

740359 

3-20 

921774 

1-39 

8 i 8585 

4-53 

181416 ; 

38 

23 

74 o 55 o 

3 -19 

921691 

1 • 3 g 

818860 

4-58 

181140 

37 

24 

740742 

3 • 19 

921607 

1 -39 

819135 

4-58 

1 8 o 865 

36 

25 

740934 

3-19 

• 921624 

1 -39 

819410 

4-58 

180590 

35 

26 

74 H 25 

3-19 

921441 

1-39 

819684 

4-58 

1 8 o 3 16 

34 

27 

74 i 3 i 6 

3-19 

921357 

1-39 

819969 

4-58 

180041 

33 

28 

741 5 o 8 

3-18 

921274 

1 - 3 q 

820234 

4-58 

179766 

3 r 

29 

741699 

3.18 

921190 

1 -39 

820608 

4-67 

17949 2 

3 i 

3 o 

741889 

3.18 

921107 

1-39 

820783 

4.57 

1 79 21 7 

3 o 

3 1 

9-742080 

3 * 18 

9-921023 

1-39 

9-821067 

4-67 

10-178943 

20 

32 

742271 

3 -18 

920039 

1 - 4 o 

82 i 332 

4-67 

178668 

28 

33 

742462 

3-17 

920856 

1 - 4 o 

821606 

4.57 

178394 

27 

34 

742662 

3-17 

920772 

1 - 4 o 

821880 

4.57 

178120 

26 

35 

742842 

3-17 

920688 

1 - 4 o 

822164 

4.07 

177846 

25 

36 

743o33 

3-17 

920604 

1 - 4 o 

822429 

4.57 

177671 

24 

37 

743223 

3-17 

920620 

1 - 4 o 

822703 

4-67 

177297 

23 

38 

7434 i 3 

3 • 16 

920436 

1 - 4 o 

822977 

4-56 

177028 

22 

3 g 

743602 

3 -i 6 

920352 

1 - 4 o 

823260 

4-56 

176700 

21 

4 o 

743792 

3 -16 

920268 

1 -40 

823524 

4-56 

176476 

20 

4 1 

9-743982 

3 -16 

9-920184 

1 - 4 o 

9-823798 

4-56 

io-176202 

19 

42 

744 i 7 i 

3 -16 

920099 

1 - 4 o 

824072 

4-56 

175928 

l 3 

43 

744361 

3 • 1 5 

920010 

1 - 4 o 

824346 

4-56 

175655 

17 

44 

74455o 

3 • 1 5 

919931 

1 -41 

824619 

4-56 

175381 

l6 

45 

744739 

3 • 1 5 

919846 

i- 4 i 

82489! 

« 4-56 

175107 

1,0 

46 

744928 

3 -1 5 

919762 

1 * 4 i 

825 i 66 

4-56 

174334 

14 

47 

740117 

3 -1 5 

9 1 9 6 77 

1 -41 

825439 

4-55 

174661 

i 3 

48 

7453o6 

3 -14 

919693 

1 - 4 i 

82571! 

4-55 

174287 

1 

4.9 

745494 

3 -i 4 

919508 

1 - 4 i 

826986 

4-55 

174014 

XI 

5 o 

745683 

3 • 14 

919424 

i- 4 i 

826269 

4-55 

*73741 

1 *° 

5 i 

9-746871 

3 • 14 

9-919339 

1 - 4 i 

9-826632 

4-55 

10-173468 


52 

746069 

3 -14 

919264 

i- 4 i 

826806 

4-oo 

173196 


53 

746248 

3 • 1 3 

919169 

i- 4 i 

827078 

4-55 

172922 

7 

z 

04 

746436 

4-13 

919080 

i* 4 i 

827301 

4-55 

172649 

0 

£ 

55 

746624 

3-13 

919000 

1 - 4 i 

827624 

4-55 

172376 


56 

746812 

3 • 1 3 

918915 

I -42 

827897 

4-54 

172103 

4 

5~i 

748999 

3 • 1 3 

9 i 883 o 

1 -42 

828170 

4-54 

171830 

3 

58 

747*87 

3-12 

918740 

1 -42 

82844? 

4-54 

171 558 

2 

5 g 

747374 

3-12 

918609 

1 -42 

828716 

4-54 

171280 

I 

60 

747562 

3-12 

91867 4 

1-42 

828987 

4-54 

171018 

0 


Cosine 

1 D. 

1 Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


18 (56 DEGREES.) 






































































62 


(34 DEGREES.) A TABLE OF LOGARITHMIC 


M, 


Sine 


D. 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 
12 
i 3 
U 

1 5 

16 

*7 

18 

19 

20 

21 

22 

23 

24 
20 
26 
2 
2 

3 ? 

3 1 

32 

33 

34 

35 

36 

37 

38 

39 

40 


9-747562 

747749 

747936 

748123 

7483 io 

748497 

748683 
748870 
749066 
74924 3 
749429 

9-749615 

749801 

749987 

760172 

700358 

760643 

750729 

700914 

761099 

761284 

9-751469 

75 i 654 

751839 

752023 

762208 

762392 

762576 

702760 

752944 

753128 

9 - 7533 i 2 

753495 

753679 

763862 

754046 

754229 

764412 

764696 

754778 

764960 


4 1 9 

42 

43 

44 

45 ] 

46 

47 

48 

£ 

5 1 

52 

53 

54 

55 

56 

57 

58 

60 


755 i 43 

755326 

7555o8 

766690 

700872 

706004 

706236 

766418 

766600 

766782 

•766963 

707144 

767326 

767607 

757688 

757869 

758 o 5 o 

75823 o 

758411 
758691 


Cosine 


3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 

3 


12 

12 

12 

I T 
I T 
I 1 

I I 

II 
10 
10 
IC 

10 

10 

°9 

°9 

°9 

°9 

°5 

08 

oS 

08 

08 

08 

08 

07 

07 

07 

07 

07 

06 

06 

06 

06 

06 

o 5 

o 5 

o 5 

o 5 

o 5 

04 

04 

04 

04 

04 

04 

o 3 

o 3 

o 3 

o 3 

o 3 

02 

02 

02 

02 

02 

01 

01 

01 

01 

01 

01 


Cosine 


D. 


xung. 


JO. 


9-918574 
918489 
91 8404 

91 83 18 
918233 
918147 

918062 

917976 

917891 

917805 

917719 

9-917634 
917048 
917462 
917376 
917290 
917204 
917118 
917032 
916946 
916869 

9-916773 

916687 
9i6600 
916614 
916427 
916341 
916254 

916167 

916081 

915994 

9-915907 
915820 
916733 
916646 
915069 
916472 
91 5385 
916297 
915210 
91 5 1 23 

9 - 9 i 5 o 35 
914948 
914860 
914778 

914686 

914^98 

914310 

914422 

914334 

914246 

9-914158 
914070 
913982 
913894 I 
913806 
913718 
9 i 363 o I 
9 i 354 i I 
9 i 3453 1 
91 3365 | 


42 

42 

42 

42 

42 

42 

42 

43 
43 
43 
43 

43 

43 

43 

43 

43 

43 


44 

44 

44 

44 

44 

44 

44 

44 

44 

45 
45 
45 

45 

45 

45 

45 

45 

45 

45 

45 

45 

46 

46 

46 

46 

46 

46 

46 

46 

46 

46 

47 

47 

47 

47 

47 

47 

47 

47 

47 

47 

47 


Sine 


D. 


9-828987 

829260 

829532 

829806 
830077 
83 o 349 
83o62i 
83 o 8 9 3 
83 11 65 
831437 
831709 

9• 83 1981 
832253 
832525 
832796 
833 o 68 
833339 
8336 11 
833882 
834 1 54 
834425 

9•834696 
834967 
835238 
835509 
835780 
836 o 5 i 
836322 
836693 
836864 
837134 

9-837406 

837675 

837946 

838216 

838487 

838767 

839027 

839297 

839668 

839838 

9-840108 

84 o 3 7 8 

840647 

840917 

841187 

841457 

841726 

841996 

842266 

842535 

9 842805 
843074 
843343 
843612 
843882 
844161 
844420 
844689 
844958 
846227 


D. 


4*54 

4-54 

4-54 

4-54 

4-54 


Cotang. 


53 

53 

53 

53 

53 

53 


4-53 
4-53 
4 • 53 
4-53 
4-62 
4-62 


10-171013 

170740 
170468 

170196 

169923 

169651 

169379 

169107 

168835 

168563 

168291 

io-168019 

167747 
167475 
167204 
166932 
166661 


60 

I is 

57 

56 

55 

54 

! 53 

52 

5 i 

5o 

49 

48 

47 

46 

45 

44 


Cotang. 


4-52 

166389 ! 

43 

4-02 

166118 

42 

4-52 

166846 

4i 

4-52 

165575 

4o 

4-52 

io-i653o4 

3 9 

4-02 

i65o33 

38 

4-52 1 

164762 

37 

4-52 j 

164491 

36 

4-oi 

164220 

35 

4-5i 

163949 

34 

4 -5i 

163678 

33 

4 • 5 1 

163407 

32 

4 - 5 1 

1 63 1 36 

3i 

4-5 1 j 

162866 

3o 

4 * 5 1 

io -162695 

29 

4-5i 

162325 

28 

4 - 5i 

162054 

27 

4-5i 

161784 

26 

4-5o 

161 5i3 

25 

4-5o 

161243 

2 4 

4-5o 

16097 3 

23 ! 

4-5o 

160703 

22 

4-5o 

160432 

21 

4-5o 

160162 

20 

4 - 5o 

io -159892 

IO 

4-5o 

159622 

IO 

4-5o 

159353 

17 

4-49 

169083 

l 6 

4-49 

i588i3 

i5 ■ 

4-49 

158543 

14 

4-49 

158274 

i3 

4.49 

i58oo4 

12 

4-49 

107734 

11 

4.49 

157466 

10 

4-49 

4-49 

10-157195 

156926 

§ 

4-49 

156657 

7 

4-49 

156388 

6 

4-48 

i56i 18 

5 

4-4? 

155849 

4 

4-48 

1 5558o 

3 

4'48 

1 553 11 

2 

4-48 

1 55o42 

1 1 

4-48 

164778 

i 0 

D. 

Tang. 

1 M. _ 


(55 DEGREES.) 














































































SINES AND TANGENTS. (35 DEGREES.) 


53 


u . 

Sine 

IX | 

Cosine 

D. 

rang. 

D. 

0 

9-758591 

3 -oi 

9-91 3365 

i -47 

9-846227 

4-48 

i 

768772 

3 -oo 

913276 

i -47 

846496 

4.48 

2 

758962 

3 -oo 

913187 

1 -48 

846764 

4-43 

3 

759132 

3 -oo 

913099 

1-48 

846 o 33 

4-48 

4 

769312 

3 -oo 

9i3oio 

1 -48 

846302 

4.48 

5 

759492 

3 -oo 

912922 

1 -48 

846670 

4-47 

6 

759672 

2-99 

912833 

1-48 

846839 

4-47 

7 

769862 

2-99 

912744 

1-48 

847107 

4-47 

8 

760031 

2-99 

912655 

1-48 

847376 

4-47 

9 

760211 

2-99 

912566 

1-48 

847644 

4-47 

10 

760390 

2-99 

912477 

1 -48 

847913 

4-47 

ii 

9-760569 

2-98 

9-912388 

1-48 

9-848181 

4-47 

12 

760748 

2-98 

912299 

1-49 

848449 

4-47 

i 3 

760927 

2-98 

912210 

1 -49 

848717 

4-47 

i 4 

761106 

2-98 

912121 

1 -49 

848986 

4-47 

i 5 

761285 

2-98 

912031 

1-49 

8492.64 

4-47 

16 

761464 

2-98 

911942 

1 -49 

849522 

4-47 

17 

761642 

2-97 

911 853 

1 -49 

84.979° 

4.46 

18 

761821 

2-97 

911763 

1 -49 

85 oo 58 

4-46 

19 

7 6i 999 

2-97 

9 h 674 

1 -49 

85 o 325 

4.46 

20 

762177 

2-97 

911584 

1-49 

860693 

4.46 

21 

9-762356 

2-97 

9-911495 

1-49 

9-860861 

4-46 

22 

762534 

2-96 

91i 4 o 5 

1 -49 

861129 

4.46 

23 

762712 

2-96 

911 3 1 5 

1 - 5 o 

861396 

4-46 

24 

762889 

2-96 

911226 

1 - 5 o 

861664 

4.46 

25 

763067 

2-96 

9111 36 

1 - 5 o 

85 iq 3 i 

4-46 

26 

763245 

2-96 

911046 

1 - 5 o 

802199 

4-46 

2 7 

763422 

2-96 

910906 

1 - 5 o 

852466 

4-46 

28 

763600 

’2-95 

910866 

1 - 5 o 

852733 

4-45 

29 

763777 

2-g5 

910776 

1 - 5 o 

853 ooi 

4-45 

3 o 

763964 

2-96 

910686 

1 - 5 o 

853268 

4-45 

3 i 

9-764131 

2-95 

9-910696 

1 - 5 o 

9-853535 

4-45 

32 

764308 

2-95 

910606 

1 - 5 o 

853802 

4-45 

33 

764485 

2-94 

91041 5 

1 - 5 o 

854069 

4-45 

34 

764662 

2-94 

910825 

1 • 5 1 

854336 

4-45 

35 

764838 

2-94 

910235 

1 - 5 1 

804603 

4 - 4 ° 

36 

765 oi 5 

2-94 

910144 

1 • 5 1 

854870 

4-45 

^7 

765191 

2-94 

910054 

1 - 5 1 

855 137 

4-45 

38 

765367 

2-94 

909963 

1 - 5 i 

855404 

4-45 

3 9 

765544 

2-93 

909873 

1 • 5 1 

85.0671 

4-44 

4 o 

765720 

2-9.3 

909782 

1 • 5 1 

855938 

4-44 

4 i 

9.765S96 

2-93 

9-909691 

1 - 5 1 

9-866204 

4-44 

42 

766072 

2-93 

909601 

1 - 5 1 

80647 1 

4-44 

43 

766247 

2-93 

909810 

1 - 5 1 

866737 

4-44 

44 

766428 

2-93 

909419 

1 • 5 1 

857004 

4-44 

I 45 

766698 

2-92 

909328 

1-62 

857270 

4-44 

46 

766774 

2-92 

909237 

I -52 

867537 

4-44 

47 

766949 

2-92 

909146 

I -52 

867803 

4 • 44 

48 

767124 

2-92 

909066 

1 -52 

868069 

4-44 

49 

767300 

2-92 

908964 

I -52 

858336 

4-44 

5 o 

767473 

2-91 

908873 

I -52 

858602 

4-43 

5 i 

9-767649 

2-91 

9-908781 

1-62 

9-858868 

4*43 

52 

767824 

2-91 

908690 

I -62 

809134 

4 - 43 

53 

767999 

2-91 

908699 

1-52 

869400 

4-43 

54 

76817.3 

2-91 

908607 

I -52 

809666 

4-43 

55 

768348 

2-90 

908416 

i -53 

869932 

4-43 

56 

768522 

2-90 

90S324 

1 -53 

860198 

4-43 

57 

768697 

2-90 

908288 

1 -53 

860464 

4-43 

53 

768871 

2-90 

908141 

1 -53 

860730 

4 - 43 

59 

769045 

2-90 

908049 

i -53 

860995 

4-43 

60 

769219 

2-90 

907958 

i -53 

861261 

4-43 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 


(54 DEGREES.) 


— 

"- 1 iq 

Cotang. 


10-164773 

60 

154604 

59 

164236 

58 , 

103967 | 

67 

153698 

56 

15343 o 

55 

153161 

54 

162893 

53 | 

162624 

52 

i 52,556 

01 

152087 
io-161819 

5o 

49 

48 

151551 

i 5 i 283 

47 

161014 

46 

160746 

45 

100478 

44 

i 5 o 2IO 

43 

149942 

42 

149676 

4i 

149407 

4o 

10-149139 

39 

148871 

38 

148604 

3 7 

148336 

36 

148069 

35 

147801 

34 

147534 

33 

147267 

32 

146999 

31 

1467)2 

3o 

io-i 46465 

29 

146198 

28 

145901 

27 

145664 

26 

145397 

25 

145 too 

24 

144863 

2,3 

144596 

22 

144329 

21 

144062 

20 

10-143796 

19 

143529 

18 1 

143260 

17 ! 

142996 

1427)0 

161 

i5 

142463 

14 i 

142197 

i3 J 

141981 

12 1 

141664 

11 

141398 

10 

io-14113 2 

9 

140866 

8 

140600 

7 

i 4 o 334 

6 

140068 

5 1 

139802 

4 

139686 

3 

1,89270 

2 

139005 

138739 

1 

0 

Tang. 

M. 
































































54 


(36 DEGREES.) A TABLE OF LOGARITHMIC! 


M. 

Sine 

D 

i Cosine 

i D - 

Tang. 

i D - 

Cotang. 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1 3 

1 4 

1 5 

16 

3 

J 9 

20 

21 

22 

23 

24 

25 

26 

27 

28 

5 9 

3 0 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

40 

4 1 

42 

43 

44 

45 

46 

47 

48 

to 

5 i 

5 s 

53 

54 

55 

56 

57 

58 

5 9 

60 

j 9-769219 

769393 

769666 

769740 

769913 

770087 

770260 

770433 

770606 

770779 

770952 

9*771125 

771298 

771470 

771643 

771815 

771987 

772159 

77233 i 

7725 o 3 

772675 

9-772847 

773018 

773190 

77336 i 

773533 

773704 

773875 

774046 

774217 

774388 

9*774558 

774729 

774899 

776070 

776240 

77 5 4 io 

77558 o 

775750 

775920 

776090 

9*776259 

776420 

776598 

776768 

776937 

777106 

777275 

777444 

777613 

77778 i 

9 ' 77796 ° 
778119 
778287 
778455 
778624 
778792 
778960 
779128 
779295 
779463 

2*90 

2*89 

2*89 

2*89 

2*89 

2*89 

2*88 

2*88 

2*88 

2*88 

2*88 

2*88 

2*87 

2*87 

2*87 

2*87 

2*87 

2*87 

2*86 

2*86 

2*86 

2*86 

2*86 

2*86 

2*85 

2*85 

2*85 

2*85 

2*85 

2*85 

2*84 

2*84 

2*84 

2*84 

2*84 

2*84 

2*83 

2*83 

2*83 

2*83 

2*83 

2*83 

2*82 

2*82 

2*82 

2*82 

2*82 

2*81 

2 • 8l 
2*8l 

2 • 81 

2*81 

2*8l 

2* 80 

2* 80 

2* 80 

2* 80 

2 • 80 

2* 80 
2*79 

2*79 

9*907068 

907866 

907774 

907682 

907690 

907498 

907406 

907314 

907222 

907129 

907037 

9•906945 
906862 
906760 
906667 
906575 
906482 
906389 
906296 
906204 
906m 

9*906018 

905925 

9 o 5832 

906739 

905646 

905552 

9o5459 

9 o 5366 

906272 

906179 

9 * 9 o 5 o 85 

90499 2 

904898 

904804 

904711 

904617 

904523 

904429 

904335 

904241 

9*904147 

9o4o53 

903959 

9 o 3 o 64 

903770 

903676 

9 o 358 i 

903487 

903392 

903298 

9 * 9 o 32 o 3 

9 o 3 io 8 

9 o 3 oi 4 

902919 

902824 

902729 

902634 
902539 
902444 
902349 ; 

i *53 

i *53 

i *53 

i *53 

i *53 

i *53 

i *53 

1*64 

i *54 

i *54 

1.54 

1*54 

1 *54 
i *54 
i *54 
i *54 

1 *54 
i *55 
i *55 
i *55 

1 *55 

i *55 

i *55 

i *55 

i *55 

i *55 

i *55 

i *55 

i *56 

i *56 

1 - 56 

1*56 

i *56 

i *56 

i *56 

i *56 

i *56 

i *56 

1*57 

i* 5 7 

1 -67 

1 *57 
i* 5 7 
i* 5 7 

'I 7 

'I 7 

'I 7 

1*57 

i *58 

i *58 

1 *58 
i *58 
i *58 
i *58 
i *58 
i *58 

1 *58 

1 * 5 g 

1 *59 

1 *59 

9*861261 

861527 

861792 

862008 

862323 

862689 

862864 
863 i19 
863385 
86365 o 
8639 i 5 

9*864180 
864440 
864710 
86497 s 
866240 
8655 o 5 
865770 
866 o 35 
8663 00 
866564 

9*866829 

867094 

867358 

867623 

867887 

8681 52 

868416 

868680 

868940 

869209 

9*869473 
869737 
870001 
870265 
870529 
870793 
871057 
871321 
871 585 : 
871849 i 

9*872112 

872376 

872640 

872903 

873167 

873430 

873694 

873967 

874220 

874484 

9*874747 

875010 

876273 

875536 

876800 

876063 

876326 

876689 

876861 

877114 

4*43 

4*43 

4*42 

4*42 

4*42 

4*42 

4*42 

4*42 

4*42 

4*42 

4*42 

4*42 

4*42 

4*42 

4 * 4 i 

4 * 4 i 

4 * 4 i 

4 * 4 i 

4 * 4 i 

4 * 4 i 

4 * 4 i 

4 * 4 i 

4 * 4 i 

4 - 4 i 

4 * 4 i 

4 * 4 i 

4.40 

4 - 4 o 

4 * 40 
4 * 4 o 
4 * 4 o 

4.40 

4.40 

4.40 

4.40 

4.40 

4.40 

4.40 

4*40 

4.40 

4*39 

4 * 3 9 

4 * 3 9 

4 * 3 9 

4 - 3 , 

4*39 

4 * 3 9 

4 * 3 9 

4 * 3 9 

4.39 

4*39 

4 * 3 9 

4 * 3 9 

4*38 

4*38 

4*38 

4*38 

4*38 

4*38 

4*38 

4*38 

10*138739 

138473 

138208 

137942 

1 37677 

137411 
137146 

1 3688 1 
i 366 i 5 
i 3635 o 
i 36 o 85 

j10 *135820 
135555 
135290 
i 35 o 25 
134760 

1 3449 s 

i 3423 o 

1 33 9 65 
133700 
133436 

io*133171 

132906 

132642 
132377 
13211 3 
131848 
r 3 i 584 
i 3 i 32 o 
i 3 io 55 
130794 

io* i3o527 
i 3 o 263 
129909 
129735 
129471 
129207 
128943 
128679 
128415 j 
1281 5 1 

10*127888 
127624 
127360 
127097 ■ 
126833 

126670 

1 263 o 6 

126043 
125780 

1 255 16 

10 -125253 

124990 
124727 
124464 
124200 
123937 
123674 
123411 

128149 

122886 

60 

s 9 
58 , 

: 5 7 
56 
55 
54 

53 

52 

5 i 

5 o 

40 
48 

47 

46 

45 

44 

43 

42 

4 1 

40 

3 9 

38 

37 

36 

35 

34 

33 

32 

3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

i 5 

14 

i 3 

12 

11 

10 

Q 

8 

7 

6 

5 

4 

3 

2 

1 

0 

.. 

Cosine 

D. 

Sine 

D. 

' D. 


M. 


(53 DEGREES.) 













































































SINES AND TANGENTS. (37 DEGREES.) 


55 


M. 

o 

1 

2 

3 

4 

5 

6 


Sine 


9-779463 

77963i 

77979 s 

779966 

70 oi 33 
78o3oo 
780467- 
780634 
780801 
780968 

781134 

11 1 9-781301 

12 781468 
781634 


7 

8 

9 

10 


13 

14 

15 

16 

n 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

59 

00 

31 

32 

33 j 

34 

35 

36 

37 

38 

3 9 

40 

j 4 i 

j 42 

43 

44 

45 
j 46 
i 47 

4 « 

: 49 


781800 

781966 

782132 

782298 

782464 

782630 

782796 

9-782961 

783127 

783292 

7 83458 

783623 

783788 

,783953 

784118 

784282 

784447 

9-784612 

784776 
784941 
7851o 5 
785269 
785433 j 
785597 ; 
785761 | 
785926 
786089 | 

9-786252 
786416 j 
786579 
786742 i 
786906 
"■87069 
787232 1 


D. 


787557 ; 
787720 


2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2' 
2 
2 
2' 
2 - 
2 - 
2 - 
2 ■ 
2 ■ 
2- 

2- 

2- 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2 

2' 


•79 

•79 

■79 

■79 

■ 7 ? 

.78 

■78 

- 7 s 

,78 

78 

.78 

■77 

■77 

77 

77 

77 

77 

76 

76 

76 

76 

76 

75 

7 5 

75 

75 

75 

75 

74 

74 

•74 

•74 

•74 

•74 

-73 

• 7 s 

-73 

•73 

.73 

•73 

.72 
.72 
.72 
.72 
.72 
■ 72 
■ 7 i 
71 
71 
7 i 


Cosine 


9-902349 

902253 

902158 

902063 

901967 

901872 

901776 

901681 

90 i 585 

901490 

901394 

9-901298 

901202 

901106 

901010 

900914 

900818 

900722 

900626 

900529 

900433 

9-900337 

900240 

900144 

000047 

899951 

899854 

899757 

899660 

899664 

899467 

9-89937o 
899278 
899176 
899078 
89S981 

898884 

898787 

898689 

898692 

898494 

9-898397 
898299 
898202 
898io 4 
898006 
897908 
897810 
897712 
897614 
897516 


D. 


109 
1-59 
1 -59 
1 -69 

I 9 

.59 

I 9 

& 


1 -6o 
1 -6o 
1 -6o 
1 -6o 
1 -6o 
1 -6o 
1 -6o 
1 -6o 
1 -6o 
1 • 61 

1 -6i 
1 -6i 
1 -6i 
1 -6i 
1 -6i 
1 • 61 
1 -6i 
1 -6i 
1 • 61 
1 -62 

1 -62 

1 -62 
1 -62 
1 -62 
1 -62 
1 -62 
1 -62 
1 -62 
1 -62 
1 -63 

i -63 
1 -63 
i -63 
i -63 
i -63 
1 -63 
1 -63 
1 -63 
i -63 
i -63 


51 

9-787883 

2-71 

9-89741s j 

1 -64 

52 

788045 

2-71 

897820 j 

1 -64 

53 

788208 

2-71 

897222 J 

1 -64 

54 

788370 

2-70 

897123 

1 -64 

55 

788532 

2-70 

897026 

1 -64 

56 

788694 

2-70 

896926 1 

1 -64 

5 7 

788856 

2-70 

896828 1 

1 -64 

58 

789018 

2-70 

896729 1 

1 -64 

59 

789180 

2-70 

896631 

1 -64 

60 

789342 

2-69 

896532 1 

1-64 


Cosine j 

D. 

Sine i 

D. 


Tang. 

D. 

j Cotang. 


9-877114 

4’ 38 

10-122886 

60 

s 77377 

4-38 

122623 


877640 

4-38 

122360 

877903 

878165 

4-38 

4-38 

122097 

I 2 i 835 

57 

56 

878428 

4-38 

121672 

55 

878691 

878953 

4-38 

4-37 

121309 

121047 

54 

53 

879216 

4-37 

120784 

52 

879478 

4-37 

120522 

5 i 

879741 

4-37 

120259 

5 o 

9 - 88 ooo 3 

4-37 

io-119997 

49 

880266 

4-37 

H 9735 

43 

88 o 528 

4-37 

119472 

47 

880790 

4-37 

119210 

46 

881062 

4-37 

118948 

45 

88i 3 14 
881 5 7 6 

4-37 

n 8686 

44 

4-37 

118424 

43 

881839 

4-37 

118161 

42 

882101 

4-37 

117899 

117687 

4 i 

882363 

4-36 

4 o 

9-882625 

4-36 

10-117375 

39 

882887 

4-36 

117113 

38 

883148 

4-36 

11 6852 

s 7 

8834 io 

4-36 

116690 

36 

8836 7 2 

4-36 

116328 

35 

883 9 34 

884196 

4-36 

116066 

34 

4-36 

11 58 o 4 

33 

884457 

4-36 

11 5543 

32 

884719 

4-36 

116281 

3 i 

884980 

4-36 

I I 5 o 20 

3 o 

9-886242 

4-36 

10-I 14758 

20 

8855 o 3 

4-36 

114497 

28 

886765 

4-36 

114235 

2 7 

886026 

4-36 

I13974 

26 

886288 

4-36 

113712 

25 

886549 

4-35 

II3461 

24 

886810 

4-35 

113190 

23 

887072 

4-35 

112928 

22 

887333 

4-35 

112667 

21 

887694 

4-35 

II2406 

20 

9-887855 

4-35 

10-112146 

IO 

888116 

4-35 

III884 

10 

888377 

4-35 

I11623 

J 7 

888689 

4-35 

i t i 36 i 

16 

888900 

4-35 

111100 

i 5 

889160 

4-35 

110840 

14 

889421 

4*35 

110679 

i 3 

889682 

4-35 

iio 3 i 8 

12 

889943 

4-35 

110067 

11 

890204 

4*34 

109796 

10 

9-890465 

4-34 

to-109535 

o 

890725 

4*34 

109275 

8 • 

890986 

4-34 1 

100014 

7 

891247 

4-34 

108753 

6 

891607 

4-34 

108493 

5 

891768 

4-34 

108232 

4 

892028 

4-34 

107972 

3 

892289 

4-34 

107711 

2 

892649 

4-34 

107461 

1 

89281c 

4-34 

107190 

0 

Cotang. 

D. 

Tang. 

M. 


(52 DEGREES.) 









































































56 


(38 DEGREES.) A TABLE OF LOGARITHMIC 



Sine 

D. 

Cosine 

D. 

Tang. 

D. ! Cotang. 


0 

1 

2 1 

3 

4 

5 

6 

I 

9 

10 

II 

12 

1 3 

1 4 

15 

16 

17 

18 

1 9 

20 

21 

22 

23 

24 
20 

26 

27 

28 

3 ? 

3 1 

32 

33 

34 

35 

36 

37 

38 

3 9 

40 

4 1 

42 

43 

44 

45 

46 

47 
4 » 

S 

5 1 

52 

53 

54 

55 

56 

5 : 

58 

5 9 

60 

9-789342 
789504 1 
789665 | 
789827 i 
789988 
790149 

790310 ! 

790471 

790632 

790793 

790954 

9-79111 5 
791275 
791436 
791696 

79^7 

79 * 9*7 

792077 

792237 

792897 

792557 

9-792716 
792876 
793o35 
7,3195 
793354 
7935 i 4 
793673 
793832 
79399 1 
794 i 5 o 

9* 7943 o 8 

794467 

794626 

794784 
794942 
7 9 5'.01 
796269 

796417 

795575 

795733 

9-795891 

796049 

796206 

796364 
796521 
796679 
796836 
796993 
7971 DC 
797307 

1 9-797464 

797621 

797777 

797934 

1 798091 

798247 
798408 
798560 
79 s 7 i 6 
798872 

2-69 
2-69 
2-69 
2-69 
2-69 
2-69 1 

2-68 
2-68 
'2-68 
2-68 
2-68 

2-68 

2-67 

2-67 

2-67 

2-67 

2-67 

2-67 

2-66 

2-66 

2-66 

2-66 

2-66 

2-66 

2-65 

2-65 

2-65 

2-65 

2-65 

2-65 

2-64 

2-64 

2-64 

2-64 

2-64 

2-64 

2 • 64 
2-63 
2-63 
2-63 
2-63 

2-63 

2-63 

2-63 

2-62 

2-62 

2-62 

2-62 

2-62 

2-6i 

2 • 6l 

2 -6l 

2 -6l 
2-6l 

2 • 6l 
2-6l 

2 • 6l 

2- 60 

2 ■ 60 

2 • 60 

2 -6o 

9-896532 

896433 

896335 

896236 

896137 

896038 

896939 

895840 

890741 

895641 

895542 

9-895443 

895343 

895244 

896140 

896046 

894940 

894846 

894746 

894646 

894546 

9-894446 

894346 

894246 

894146 

894046 

893946 

893846 

893745 

893645 

893544 

9-893444 

893343 

893243 

893142 

893041 

892940 

892839 

892739 

8 9 2638 

892536 

9-892435 

892634 

892233 

892132 

892030 

891929 

801827 

891726 

891624 

891623 

9-891421 
891319 
891217 
89111 5 
891013 
890m 1 
890009 
890707 
8 qo 6 o 5 
890603 

1-64 

i -65 

i -65 

i -65 

1 -65 
i -65 
i -65 
i -65 
i -65 
i -65 
i -65 

1 -66 

i-66 

1 -66 

1 -66 

1 -66 

1 -66 

1 -66 

1 -66 

1 -66 

i-66 

1 -67 

1 -67 
1-67 
1-67 

1 -67 

1 -67 
1-67 
1-67 

1 -67 

1 -67 

1 -68 

i-68 

i-68 

i-68 

1 -68 

1 -68 

i-68 

1-68 

1 -68 
i-68 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 

1 -69 
1-69 

1 -70 

1 -70 
1-70 

1 -70 
1-70 
1-70 

1 -70 

1 -70 
1-70 

1 -70 
1-70 

9-892810 
893070 
8 9 333 i 
893591 
893861 
894111 
894371 
894632 
894892 
896102 
896412 

9-895672 

895962 

896192 

896432 

896712 

896971 

897261 

897491 

897701 

898010 

9-898270 

898560 

898789 

899049 

899308 

899668 

899827 

900086 

900346 

900606 

9-900864 
901124 
901 383 
901642 
901901 
902160 
902419 

902679 

902938 

903197 

9 - 9 o 3455 

903714 

903973 

904262 

904491 

904760 

906008 

906267 

906626 

906784 

9•906043 
906302 
906060 
906819 
907077 
907366. 
907694 
907802 
908111 
908369 

4 • 34 
4-34 
4-34 
4-34 

4 • 34 

4-34 

4-34 

4-33 

4-33 

4-33 j 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-33 

4-32 

4*32 

4-32 

4-32 

4-32 

4-32 

4-32 

4 - 3 q 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4-32 

4 - 3 1 

4 • 3 1 

4 * 3 1 

4 * 3 1 

4 • 3 1 

4* 3 1 

4 • 3 1 

4 * 3 1 
| 4 - 3 i 
| 4 • 3 1 

4 * 3 1 

4 - 3 1 
4 - 31 

; 4 - 31 

4* 31 
! 4 - 3 1 

4 • 31 

4 *3 1 

4 - 3 1 
4 - 3 o 
j 4 - 3 o 

10-107190 

106960 

106609 

106409 
106149 
105889 
105629 
io 5368 
io 5 io 8 
104848 
104588 

10 -104328 
104068 
io 38 o 8 
io 3548 
103288 
103029 
102769 
102609 
102249 

101990 

10-101730 

101470 

101211 

100961 

100692 

100432 

100173 

099914 

099654 

099395 

10-099136 

098876 

098617 

098358 

098099 

097840 

097681 

097321 

097062 

096803 

10-096645 

096286 

096027 

096768 

096009 

096260 

094992 

094783 

094474 

094216 

10-093957 

093698 

093440 

093181 

092923 

092664 

092406 

092148 

091889 

4 091631 

60 

5 9 

58 

57 

56 

55 

04 

53 

52 

5 i 

5 o 

49 

48 

47 

46 

45 

44 

43 

42 

41 

40 

3 9 

38 

3 - 

36 

35 

34 

33 

32 •' 
3 i 

3 o 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

*9 

*7 

l6 

i 5 
*4 - 
i 3 

11 

1 r 

1,* 

7 

6 

5 

4 

3 

2 

1 

p 

- * 

Cosine 

I). 

Sine I). 

1 Cotang, i D. 

Tang. 



(51 DEGREES.) 



































































SINES AND TANGENTS. (39 DEGREES.; 57 


M. 

Sine 

D. i 

0 

9-798872 

2 -6o 

I 

799028 

2 -6o 

2 

799184 

2 -6o 

3 

799339 

2-69 

4 

5 

799493 

7996D1 

2-69 

2-69 

6 

799806 

209 

7 

799962 

2-69 

8 

800117 

2-69 

9 

800272 

2-58 

10 

800427 

2-58 

ii 

9-800682 

2 - 5 S 

12 

800787 

• 2-58 

i 3 

800892 

2-58 

14 

801047 

2-58 

ID 

801201 

2-58 

16 

801 356 

2.57 

17 

8 oi 5 ii 

2 - 5 ~l 

18 

8 oi 665 

2 - 5 -J 

19 

801819 

2-67 

20 

801978 

2 - 5 j 

21 

9-802128 

2 - 5 ~i 

22 

802282 

2-56 

23 

802486 

2-56 

24 

802D89 

2-56 

2 D 

802740 

2 • 56 

26 

802897 

2-56 

2 7 

8 o 3 o 5 o 

2 • 56 

28 

803204 

?-56 

29 

8 o 33 d 7 

2-55 

00 

8 o 35 ii 

2 • DD 

3 i 

9•803664 

2-55 

32 

803817 

2-55 

33 

80897° 

2-55 

34 

804123 

2-55 

35 

804276 

2-D 4 

36 

804428 

2-54 

3 7 

S04D81 

2-34 

38 

804784 

2-54 

3 9 

804886 

2-54 

4 o 

800089 

2-54 

4 i 

9• 8 o 5 191 

2-54 

42 

800843 

2-53 

43 

8o549° 

2-53 

44 

8 o 5647 

2-53 

45 

800799 

2-53 

46 

806961 

2-53 

47 

806 1 o 3 

2-53 

48 

806204 

2-53 

49 

806406 

2-52 

5 c 

So 6557 

2-52 

5i 

9 806709 

2 -52 

52 

806860 

2-52 

53 

807011 

2-52 

54 

807168 

2-52 

55 

8 oo 3 i 4 

2-52 

56 

807466 

2 - 51 

57 

807615 

2 • 51 

58 

807766 

2 - 5 1 

5 9 

807917 

2 * 51 

60 

808067 

2 - 5 l 


Cosmo 

D. 


Cosine 

D. 

Tang, i 

9•890603 
890400 

1 -70 

1 ■ 7 1 

9-908369 

908628 

8902 78 

i- 7 * 

908886 

890195 

1-71 

909144 

909402 

909660 

890093 

889990 

1-71 

I-7 1 

889888 

*•7* 

909918 

889180 

1-71 

910177 

889682 

i'll 

910435 

889679 

1-71 

. 910693 

889477 

i'll 

910961 

9-889874 

1 -72 

9-911209 

889271 

1 -72 

911467 

889168 

1-72 

911724 

889064 

1 -72 

911982 

888961 

1 -72 

912240 

888858 

1-72 

912498 

888755 

1 -72 

912756 

88865i 

1-72 

9i3oi4 

888548 

1-72 

913271 

888444 

i -73 

913529 

9-888341 

1-73 

9-913787 

888237 

1*73 

914044 

888 i 34 

i - i 3 

9i43o2 

888 o 3 o 

i - 7 3 

914360 

887926 

i -7 3 

914817 

887822 

i-7 3 

916076 

887718 

1 *73 

9i5332 

887614 

1 -73 

915590 

887610 

1 -73 

916847 

887406 

1-74 

916104 

9-887302 

i -74 

9-916362 

887198 

i -74 

916619 

887093 

886989 

i -74 

916877 

1-74 

917'34 

886885 

1-74 

91739 1 

886780 

1-74 

917648 

886676 

i -74 

917906 

886671 

i -74 

9i8i63 

886466 

1-74 

918420 

886362 

1 -70 

918677 

9-886207 

l 7 5 

9-918934 

886132 

1-70 

919*91 

886047 

i - 7 3 

919448 

885942 

I - 7 3 

919706 

88583 7 

I - 7 3 

919962 

885732 

1-73 

920219 J 

885627 

1-73 

92047 6 

885522 

1-73 

920733 

885416 

I -70 

920990 

885311 

I -76 

921247 

9-885205 

1-76 

9-92i5o3 

885100 

I-76 

921760 

884994 

884889 

I -76 
1-76 

922017 

922274 

884783 

[•76 

92253 o 

884677 

I -76 

922787 

884672 

1-76 

923044 

884466 

1-76 

9233oo ; 

884360 

I -76 

923557 

884254 

I'll 

9 23813 

Sine 

D. 

Jotang. ! 


D. 

Cotang. 

! : 

4 - 3 o 

10-091631 

60 

4 - 3 o 

091372 

5 9 

4 - 3 o 

091114 

58 

4 - 3 o 

090866 

^7 

4 - 3 o 

090698 

56 

4 - 3 o 

090340 

55 

4 - 3 o 

090082 

54 

4 - 3 o 

089823 

53 

4 - 3 o 

089066 

52 

4 - 3 o 

089307 

5 i 

4 - 3 o 

089049 

DO 

4 - 3 o 

10-088791 

49 

4 - 3 o 

o 88533 

48 

4 - 3 o 

088276 

47 

4 - 3 o 

088018 

461 

4 - 3 o 

087760 

45 

4 - 3 o 

087602 

44 

4 - 3 o 

087244 

43 

4-29 

086986 

42 

4-29 

086729 

4 i 

4-29 

08647 1 

40 

4-29 

io-086213 

3 9 

4-29 

086956 

38 

4-29 

080698 

37 

4-29 

o 8544 o 

36 

4-29 

o 85 i 83 

35 

4-29 

084926 

34 

4-29 

084668 

33 

4-29 

084410 

32 

4-29 

084163 

3 i 

4-29 

o 838 q 6 

3 o 

4-29 

io-o 83638 

29 

4-29 

oS 338 i 

28 

4-29 

oS 3 i 23 

27 

4-29 

082866 

26 

4-29 

082609 

25 

4-29 

082362 

24 

4-29 

082096 

23 

4-28 

081837 

22 

4.2S 

o 8 i 58 o 

21 

4-28 

o 8 i 323 

20 

4-28 

10•081066 

19 

4-28 

080809 

l8 

4-28 

o 8 o 552 

*7 

4-28 

080296 

16 

4-28 

o 8 oo 3 S 

i 5 

4-28 

079781 

*4 

4-28 

079624 

i 3 

4-28 

079267 

12 

4-28 

079010 

11 

4-28 

078753 

10 

4-28 

10-07849? 

9 

4-28 

078240 

8 

4-28 

077983 

n 

4-28 

077726 

$ 

4-28 

07747° 

D 

4-28 

077213 

4 

4-28 

076966 

3 

4-28 

076700 

Ok 

4 

4-27 

076443 

1 

4-27 

076187 

0 

D. 

Tang. 

M. 


(50 DEGREES.) 




































































58 (40 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-808067 

2 - 5 1 

9-884264 

i -77 

9 ' 9238 i 3 

4-27 

10-076187 

60 

i 

808218 

2 • 5 i 

884148 

i -77 

924070 

4-27 

076930- 

59 

2 

8 o 8368 

2 - 5 l 

884042 

1-77 

924827 

4-27 

075673 

58 

3 

808519 

2 • 5 o 

883936 

i *77 

924583 

4-27 

076417 

57 

4 

808669 

2 • 5 o 

883829 

i- 7 y 

924840 

4-27 

075160 

56 

5 

808819 

2 • 5 o 

883723 

i-W 

925096 

4-27 

074904 

55 

6 

808969 

2 - 5 o 

883617 

1/77 

9253 D 2 

4-27 

074648 

54 

7 

809119 

2 - 5 o 

8835 io 

r -77 

925609 

4-27 

074391 

53 

8 

809269 

2 - 5 o 

883404 

1-77 

925860 

4-27 

074135 

52 

Q 

809419 

2-49 

883297 

1-78 

926122 

4-27 

073878 

5 i 

IO 

809569 

2-49 

883191 

1-78 

926378 

4-27 

073622 

5 o ! 

l i 

9-809718 

2-49 

9-883084 

1-78 

9-926634 

4-27 

10-073366 

49 1 

12 

809868 

2-49 

882977 

1-78 

926890 

4-27 

073110 

48 

i 3 

810017 

2-49 

882871 

1.78 

927U7 

4-27 

072853 

47 

i 4 

810167 

2-49 

882764 

1-78 

927403 

4-27 

072597 

46 

i 5 

8 io 3 i 6 

2-48 

882657 

1-78 

927659 

4-27 

072341 

45 

16 

8 io 465 

2-48 

8 S 255 o 

1 -78 

927910 

4*27 

072085 

44 

17 

810614 

2-48 

882443 

1.78 

928171 

4-27 

071829 

43 

18 

810763 

2-48 

882336 

1-79 

928427 

4-27 

071570 

42 

19 

810912 

2-48 

882229 

1.79 

928688 

4-27 

071317 

41 

20 

811061 

2-48 

882121 

1 *79 

928940 

4-27 

071060 

40 

21 

9-811210 

2-48 

9-882014 

1.79 

9-929196 

4-27 

10-070804 

3 9 

22 

811 358 

2-47 

881907 

1.79 

929402 

4-27 

070548 

38 

23 

811607 

2-47 

881799 

1.79 

929708 

4-27 

070292 

37 

24 

81 i 655 

2-47 

881692 

1-79 

929964 

4-26 

070006 

36 

2 D 

811804 

2-47 

881 584 

1-79 

930220 

4-26 

069780 

35 

26 

811962 

2-47 

881477 

1.79 

93 o 475 

4’26 

069625 

34 

27 

812100 

2-47 

881369 

1-79 

g 3 o " 3 i 

4-26 

069269 

33 

28 

812248 

2-47 

881261 

1 -8o 

930987 

4-26 

069010 

32 

29 

812396 

2-46 

8811 53 

1 -8o 

931243 

4-26 

068757 

3 i 

3 o 

812644 

2-46 

881046 

1 -8o 

931499 

4*26 

o 685 oi 

3 o 

3 i 

9-812692 

2-46 

9-880938 

1 -8o 

9-931755 

4-26 

10-068245 

20 

32 

812840 

2-46 

88 o 83 o 

1 -8o 

932010 

4*26 

067990 

28 

33 

812988 

2-46 

880722 

1 -8o 

932266 

4-26 

067734 

27 

34 

81 3 1 35 

2-46 

88061 3 

1 -8o 

932522 

4-26 

067478 

26 

35 

8 i 3283 

2-46 

88 o 5 o 5 

1 -8o 

932778 

4-26 

067222 

25 

36 

8 i 343 o 

2-45 

880397 

1 - So 

933o33 

4-26 

066967 

24 

37 

813678 

2-45 

880289 

1 -81 

933289 

4-26 

066711 

23 

38 

813725 

2-45 

880180 

1*81 

933545 

4-26 

o 66455 

22 

3 9 

813872 

2-45 

880072 

1 • 81 

9338 oo 

4-26 

066200 

21 

40 

814019 

2-45 

879963 

1 -8i 

934 o 56 

4-26 

066944 

20 

4 i 

9-814166 

2-45 

9-879855 

1 • Si 

9-934311 

4-26 

10-065689 

19 

42 

81 43 1 3 

2-46 

879746 

1 - 81 

984567 

4-26 

o 6543 o 

18 

43 

814460 

2-44 

879637 

1 • 81 

934823 

4-26 

065177 

17 1 

44 

814607 

2-44 

879529 

1 -8i 

935078 

4-26 

064922 

ID 

45 

814753 

2-44 

879420 

1 -81 

935333 

4-26 

064667 

i 5 

46 

814900 

2-44 

879311 

1 - 81 

935589 

4-26 

064411 

i 4 

47 

8i6046 

2-44 

879202 

1-82 

930844 

4-26 

0641 56 

i 3 

48 

816193 

2-44 

879093 

1 -82 

936100 

4-26 

063900 

12 

4 9 

8 i 5339 

2-44 

878984 

1 -82 

936355 

4-26 

063645 

11 

5 o 

81 5485 

2-43 

878S75 

1-82 

936610 

4-26 

063390 

10 

5 i 

9-81 563 1 

2-43 

9-878766 

1-82 

9-936866 

4-25 

io-o 63 i 34 

9 

52 

815778 

2-43 

878656 

1-82 

937121 

4-20 

062879 

8 

53 

816924 

2 • 43 

878647 

1 -82 

937376 

4-25 

062624 

7 

1 54 

816069 

2-43 

878438 

1-82 

937632 

4-25 

o62368 

. 6 

; 55 

816216 

2-43 

878328 

1 -82 

937887 

4-25 

062113 

5 

5 t 

81 636 i 

2-43 

878219 

i -83 

938142 

4-25 

o 6 i 858 

4 

57 

I 816507 

2-42 

878109 

i -83 

938398 

4-25 

061602 

<■% 

3 

58 

81 6652 

2-42 

877999 

i -83 

938653 

4*25 

061 347 

2 

5a 

| 816798 

2-42 

877890 

i -83 

938908 

4-25 

061092 

1 

60 

i 816943 

2-42 

877780 

i -83 

939163 

4-25 

060807 

0 


| Cosmo 

1 D. 

Sine 

D. 

1 Cotang. 

i . 

' Tang. 

M. 


(49 DEGREES.) 




















































































SINES AND TANGENTS. (41 DEGREES.) 59 


M. 

Sine 

D. 

Cosine 

i D - 

Tang. 

D. 

Co tang. 


o 

9-816943 

2-42 

9.877780 

i -83 

9-939163 

4-25 

10-060837 

60 

i 

817088 

2-42 

877670 

i -83 

939418 

4-25 

o6o582 

09 

2 

817233 

2-42 

877660 

i -83 

939673 

4-25 

060327 

5 ? 

3 

817379 

2-42 

877450 

i -83 

939928 

4-25 

060072 

07 

4 

817624 

2-41 

877340 

i -83 

940183 

4-25 

009817 

56 

5 

817668 

2-41 

877230 

1 -84 

940438 

4-25 

009062 

55 

6 

817813 

2-41 

877120 

1 -84 

940694 

4-25 

059306 

54 

i l 

8 

817908 

8 i 8 io 3 

2-41 

I 2-41 

877010 

876899 

1 • 84 
1-84 

940949 

941204 

4-25 

4-25 

069061 

058796 

53 

52 

9 

; 818247 

2-41 

876789 

1-84 

941458 

4-25 

068.042 

5 i 

IO 

818392 

2 - 4 l 

876678 

1.84 

941714 

4-25 

058286 

5 o 

11 

9 * 8 i 8536 

2 -40 

9-876568 

! 1-84 

9-941968 

4-25 

io-o 68 o 32 

49 

12 

818681 

2 -40 

876467 

1-84 

942223 

4 25 

067777 

48 

i 3 

818825 

2-40 

876347 

1 -84 

942478 

4-25 

067622 

47 

i 4 

818969 

2-40 

876236 

1 -85 

9427I3 

4-25 

067267 

46 

i 5 

8191i 3 

2-40 

876125 

i -85 

942988 

4-25 

067012 

45 

16 

819267 

2-40 

876014 

i -85 

943243 

4-25 

066767 

44 

17 

819401 

2-40 

876904 

i -85 

943498 

4-25 

o 565 o 2 

43 

1-8 

819646 

2-39 

875793 

1 -85 

943762 

4-25 

006248 

42 

19 

819689 

2-39 

876682 

i -85 

944007 

4-25 

066993 

4 i 

20 

819832 

2-39 

'875571 

i -85 

944262 

4-25 

055788 

4 o 

21 

9-819976 

2-39 

9.875469 

i -85 

9-944517 

4-25 

10 •055483 

39 

22 

820120 

2-39 

875348 

i -85 

944771 

4-24 

060229 

38 

23 

820263 

2-39 

876237 

1 -85 

940026 

4-24 

0.04974 

37 

24 

820406 

2 -39 

875126 

1 -86 

946281 

4-24 

064719 

36 

20 

82o55o 

2-38 

875014 

i-86 

945535 

4-24 

064460 

35 , 

26 

820693 

2-38 

874903 

1 -86 

946790 

4-24 

064210 

34 

2 Z 

82o836 

2-38 

874791 

1-86 

946045 

4-24 

053955 

33 

28 

820979 

2-38 

874680 

i-86 

946299 

4-24 

053701 

32 

29 

821122 

2-38 

874668 

1 -86 

946554 

4-24 

00.3446 

3 i 

3 o 

821265 

2-38 

874456 

i-86 

946808 

4-24 

053192 

3 o 

3 i 

9-821407 

9.38 

9•874344 

1.86 

9-947063 

4-24 

10-052937 

29 

32 

821600 

2-38 

874232 

1-87 

9473 i 8 

4-24 

062682 

28 

33 

821693 

2-37 

874121 

1-87 

947672 

4-24 

052428 

27 

34 

82 i 835 

2-3 7 

874009 

873896 

1-87 

947826 

4-24 

002174 

26 

35 

821977 

2-37 

1-87 

948081 

4-24 

061919 

25 

36 

822120 

2-37 

873784 

1-87 

948336 

4-24 

o 5 i 664 

24 

37 

822262 

9.37 

873672 

1 -87 

948590 

4-24 

061410 

23 

38 

822404 

2-37 

873560 

1-87 

948844 

4-24 

o 5 i1 56 

22 

3 9 

822546 

2-37 

873448 

1-87 

949099 

4-24 

060901 

21 

4 o 

822688 

2-36 

87,3335 

1-87 

- 949353 

4-24 

060647 

20 

4 i 

9-822830 

2-36 

9-873223 

1-87 

9•949607 

4-24 

10-050398 

IO 

42 

822972 

2-36 

873110 

1 -88 

949862 

4-24 

o 5 oi 33 

l8 

43 

823114 

2-36 

872998 

i-88 

900116 

4-24 

049884 

17 

44 

823200 

2-36 

872886 

1-88 

950070 

4-24 

04963 cr 

l6 

45 

823397 

2-36 

872772 

1.88 

960626 

4-24 

049375 

i 5 

46 

'823039 

2-36 

872669 l 

1.88 

960879 

4-24 

049121 

14 

47 

823680 

2-35 

872647 

i-88 

901133 

4-24 

048867 

i 3 

48 

823821 

2-35 

872434 : 

1.88 

901 388 

4-24 

048612 

12 

49 

823963 

2-35 

872321 

1.88 

961642 

4-24 

048358 

11 

5 o 

824104 

2-35 

872208 

1.88 

961896 

4-24 

048104 

10 

5 i 1 

9-824245 

2-35 

9-872095 

1-89 | 

9-952160 

4-24 

10-047860 

9 

52 

824386 

2-35 

871981 1 

1-89 j 

962405 

4-24 

047095 

8 

53 

824627 

2-35 

871868 ! 

1 -89 

902609 

4-24 

047341 

7 

54 

824668 

2-34 

871760 I 

1 -89 

952913 

4-24 

047087 

6 

5 c 

824808 1 

2-34 

871641 

1 -89 

953167 

4-23 

046833 

5 

5 £ 

824949 j 

820090 1 

2-34 

871528 

1 -89 

953421 

4-23 

046579 

4 

57 

2-34 

871414 

1 -89 

953676 

4-23 

046325 

3 

58 

82523 o | 

2-34 

871301 j 

1 -89 

953929 

4-23 

046071 

2 

5 q 

825371 1 

2-34 

871187 

1 -89 

954183 1 

4-23 

045817 

1 

60 

8255 ii 1 

2-34 

87107) 

1-90 

904437 j 

4-23 

045563 

0 


Cosiue 

D. 

1 

Sine 1 

D. 

Cotang. : 

D. 

Tang. 

M. 


(48 DEGREES.) 














































































60 (42* DEGREES.' A TABLE OF LOGARITHMIC 


M. 1 

Sine 

D. 

Cosine 

D. 

Tang. 

D. j 

Cotang. 


0 

9• 8255 11 

2-34 

9-871073 

1 -90 

9-964437 

4*23 

io-o 45563 

60 

i 

82565 i 

2-33 

870960 

1 -90 

954691 

4-23 j 

o 453 o 9 

59 

2 

826791 

2-33 

870846 

1 -90 

904940 

4-23 

040000 

58 

3 

826931 

2-33 

870732 

1 -90 

966200 

4-23 

044800 

57 

4 

826071 

2-33 

870618 

1 -90 

950404 

4-23 

044546 

56 

5 

826211 

2-33 

870504 

1-90 

955707 

4-23 

044293 

55 

6 

82635 i 

2-33 

870390 

1 -90 

960961 

4-23 

044089 

54 

7 

826491 

2-33 

870276 

1 -90 

966215 

4-23 

043780 

53 j 

8 

826631 

2-33 

870161 

1-90 

966469 

4-23 

o 4353 i 

52 ] 

9 

10 

826770 

826910 

2-32 

2-32 

870047 

869933 

1-91 

1.91 

966723 

966977 

4-23 

4-23 

048277 

o 43 o 23 

5 i 

5 o 

11 

9-827049 

2-32 

9-869818 

1-91 

9-957231 

4-23 

10*042769 

49 

ID 

827189 

827328 

827467 

2-32 

869704 

1.91 

957485 

4-23 

0425 1 5 

48 

i 3 

2-32 

869589 

1.91 

907739 

4-23 

042261 

47 

i 4 

2-32 

869474 

1-91 

967993 

4-23 

042007 

46 

i 5 

827606 

2-32 

869360 

1 -91 

968246 

4-23 

o 4 h 54 

45 

16 

827745 

2-32 

869245 

1-91 

9585 oo 

4-23 

o41 5 oo 

44 

i~l 

827884 

2 • 3 I 

869130 

1-91 

958754 

4-23 

041246 

43 

18 

828023 

2 • 3 I 

86901 5 

1 -92 

939008 

4-23 

040992 

42 

19 

828162 

2 - 3 I 

868900 

1 -92 

959262 

4-23 

040738 

4 i 

20 

8283 oi 

2 • 31 

868786 

1-92 

969616 

4-23 

040484 

4 o 

21 

9-828439 

2 • 31 

9-868670 

1-92 

9-969769 

4-23 

10 •04023 X 

3 9 

22 

828678 

2 • 3 I 

868555 

1-92 

960028 

4-23 

039977 

38 

23 

828716 

2 • 31 

868440 

1-92 

960277 

4-23 

039723 

37 

24 

828855 

2 • 3 o 

868324 

1 -92 

960031 

4-23 

039469 

36 

25 

828993 

2-3o 

868209 

1 -92 

960784 

4-23 

0892i6 

35 

26 

8291 3 1 

2 - 3 o 

868098 

1 -92 

961038 

4-23 

088962 

34 

27 

28 

829269 

829407 

2 • 3 o 
2 - 3 o 

867978 

867862 

1 -93 

1 -93 

961291 
961 545 

4-23 

4-23 

038709 

038455 

33 

32 

29 

829045 

2 • 3 o 

867747 

1 -93 

961799 

4-23 

088201 

3 i 

3 o 

829683 

2 - 3 o 

867631 

1 -93 

962062 

4-23 

037948 

3 o 

3 i 

9-829821 

2-29 

9-867615 

1 -93 

9-962306 

4-23 

10-087694 

29 

32 

829969 

2-29 

867899 

i- 9 3 

962060 

4- i 3 

037440 

28 

33 

83 0097 

2-29 

867288 

1 -93 

962813 

4-23 

037187 

27 

34 

880234 

2-29 

867167 

1 -93 

963067 

4-23 

036933 

26 

35 

800872 

2-29 

867001 

i -93 

963320 

4-23 

o 3668 o 

25 

36 

830009 

2-29 

866935 

1 -94 

963074 

4-23 

086426 

24 

37 

83 o 646 

2-29 

868819 

1 -94 

963827 

4-23 

036173 

23 

38 

83 o 7 8 4 

2 • 29 

866700 

1 -94 

964081 

4-23 

030919 

22 | 

3 9 

830921 

2-28 

866586 

1 • 9 i 

964335 

4 - 23 

o 3566 o 

21 

4 o 

83 1o 58 

2-28 

866470 

1-94 

964588 

4-22 

o 354 i 2 

20 

41 

9- 83 i190 
83 1 33 2 

2 • 28 

9-866353 

1 -94 

9-964842 

4-22 

io-o 35 i 58 

j i 

42 

2-28 

866237 

1 * 9 1 

960090 

4-22 

08490 5 

x? I 

43 , 

83 1469 

2-28 

866120 

1-94 

960349 

4-22 

o 3465 1 

>7 1 

44 

83 1606 

2 • 28 

866004 

1-90 

966602 

4-22 

034398 

16 

45 

881742 

2-28 

860887 

1 -96 

965855 

4-22 

o34145 

i 5 

46 

83 1879 

2 ■ 28 

866770 

i - 9 5 

966105 

4-22 

033891 

14_ 

47 

832010 

2-27 

865653 

1-90 

966362 

4-22 

o 3363 S 

1 3 1 

48 

832 1 52 

2-27 

865536 

1-90 

966616 

4-22 

o 33384 

12 

49 

832288 

2-27 

865419 

1 -96 

966869 

4- 22 

o 33 3 1 

11 


832420 

2-27 

8653 o 2 

1 -95 

967123 

4-22 

032877 

i° ; 

5 i 

9-832061 

2 • 27 

9- 865 1 85 

1 -96 

9-967376 

4-22 

10-082624 

Q I 

52 

832697 

2-27 

865 o 68 

1 • 95 

967629 

4-22 

032371 

8 

53 

832833 

2-27 

864950 

I i- 9 5 

967883 

968136 

4-22 

0321 17 

7 

54 

882969 

2-26 

864833 

1 -96 

4*22 

o 3 i864 

6 

55 

833 o 5 

2-26 

864716 

1 -96 

9 6838 9 

4-22 

o 3 1611 

1 5 

56 

833241 

2-26 

864598 

1 -96 

968643 

4-22 

o 3 i 357 

■■ 4 

5*7 

833377 

2-26 

864481 

1 1 -96 

968896 

4-22 

o 3 11 04 

0 

0 

58 

833 oi 2 

2-26 

864363 

1 -96 

1 969149 

4-22 

o 3 o 85 i 

2 

5 9 . 

833648 

2-26 

864245 

1-96 

969403 

4-22 

o 3 o 597 

1 

60 

833783 

! 2-26 

864127 

1 -96 

969666 

4-22 

o 3 o 344 

0 j 


! Cosine 

1 D. 

Sine 

D. 

! Cotang. 

I). 

Tang. 

■ M. 


(47 DEGREES.) 













































































SINES AN'.) TANGENTS. (43 DEGREES.) 


61 


M. 

Sino 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9-833783 

2-26 

9-864127 

1 -96 

9-969666 

4-22 

10 -030344 

60 

i 

833919 

2-25 

864010 

1 -96 

969909 

4-22 

030091 

5 9 

2 

834 o 54 

2-25 

863892 

1-97 

970162 

4-22 

029838 

58 

3 

834^9 

2-25 

863774 

1-97 

970416 

4-22 

029084 

67 

4 

834320 

2-25 

863656 

1-97 

970669 

4-22 

029331 

56 

5 

83446o 

2-25 

863538 

1-97 

970922 

4-22 

029078 

55 

6 

834695 

2-25 

863419 

1-97 

971175 

4-22 

028826 

54 

7 

83473 o 

2-25 

8633 oi 

1-97 

971429 

4-22 

028671 

53 

8 

834865 

2-25 

863 1 83 

1 *97 

971682 

4-22 

028318 

52 

9 

834999 

2 • 24 

863 o 64 

1-97 

971930 

4-22 

028066 

5 i 

10 

835 i 34 

2-24 

862946 

1 -98 

972188 

4-22 

027812 

5 o 

11 

9-835269 

2-24 

9-862827 

1 -98 

9-972441 

4-22 

10-027669 

49 

12 

8354 o 3 

2-24 

862709 

1 -98 

972694 

4-22 

027306 

48 

i 3 

835538 

2-24 

862690 

1 -98 

972948 

4- 22 

027062 

47 

U 

835672 

2-24 

862471 

1-98 

973201 

4-22 

026799 

46 

i 5 

8358 o 7 

2-24 

862353 

1 -98 

973454 

4-22 

026546 

45 

16 

835941 

2-24 

862234 

1 -98 

978707 

4-22 

020293 

44 

l l 

886075 

2-23 

862 ii 5 

1 -98 

978960 

4-22 

026040 

43 

18 

836209 

2-23 

861996 

1 -98 

974213 

4-22 

026787 

42 

l 9 

836343 

2-23 

8*61877 

1 -98 

974466 

4-22 

025534 

4 i 

20 

836477 

2-23 

861758 

1.99 

974719 

4-22 

020281 

40 

21 

9- 8366 11 

2-23 

9.861 638 

1-99 

9-974973 

4-22 

10-026027 

3 9 

22 

886746 

2-23 

861 5 1g 

1 -99 

976226 

4-22 

024774 

38 

23 

836878 

2-23 

861400 

i -99 

975470 

4-22 

024621 

37 

24 

837012 

2-22 

861280 

1 -99 

975732 

4-22 

024268 

36 

2D 

837146 

2-22 

861161 

1 -99 

976986 

4-22 

024015 

35 

26 

837279 

2-22 

861041 

1-99 

976238 

4-22 

028762 

34 

27 

837412 

2-22 

860922 

1-99 

976491 

4- 22 

>23009 

33 

28 

837646 

2-22 

860802 

1 -99 

976744 

4-22 

028266 

32 

29 

837679 

2-22 

860682 

2-00 

976997 

4-22 

o 23 oo 3 

3 i 

3 o 

83 7 8 i 2 

2-22 

86 o 562 

2-00 

977260 

4-22 

0227O0 

3 o 

3 i 

9-837946 

2-22 

9-860442 

2-00 

9-977608 

4-22 

10-022497 

29 

32 

838 o 7 8 

2-21 

86 o 322 

2-00 

977766 

4- 22 

022244 

28 

33 

8382 H 

2-21 

860202 

2-00 

978009 

4-22 

021991 

27 

34 

838344 

2-21 

860082 

2-00 

978262 

4-22 

021738 

26 

35 

838477 

2*21 

869962 

2-00 

9786i 5 

4-22 

021485 

25 

36 

8386 io 

2-21 

869842 

2-00 

978768 

4-22 

021232 

24 

37 

838742 

2-21 

869721 

2-01 

979021 

4-22 

020979 

23 

38 

838875 

2-21 

869601 

2-01 

979274 

4-22 

020726 

22 

39 

839007 

2-21 

809480 

2-01 

979627 

4-22 

020473 

21 

40 

839140 

2-20 

809360 

2-01 

979780 

4-22 

020220 

20 

41 

9-839272 

2 • 20 

9■869239 

2-01 

9-980033 

4-22 

10-019967 

IO 

42 

839404 

2 • 2C 

869119 

2-01 

980286 

4-22 

OI97U 

l8 

43 

839536 

2-20 

858998 

2-01 

9 8 o 53 S 

4-22 

OI9462 

17 

44 

839668 

2-20 

868877 

2-01 

980791 

4-21 

OI9209 

l6 

45 

839800 

2-20 

858756 

2-02 

981044 

4-21 

018956 

10 

46 

839982 

2-20 

858635 

2-02 

981297 

4.21 

018703 

14 

47 

840064 

2-19 

8585 14 

2-02 

981560 

4.21 

018400 

1 3 

48 

840196 

2-19 

858393 

2-02 

981803 

4-21 

018197 

12 

49 

840828 

2-19 

868272 

2-02 

982066 

4-21 

OI7944 

11 

5 o 

840469 

2- 19 

858 1 5 1 

2-02 

982309 

4-21 

OI769J 

10 

5 i 

9-840691 

2-I9 

9-868029 

2-02 

9-982662 

4-21 

10-017438 

9 

02 

840722 

2 • 19 

867908 

2-02 

982814 

4-21 

OI7186 

8 

53 

840854 

2-19 

867786 

2-02 

983067 

4-21 

Ol 6933 

7 

54 

840 q 85 

2-10 

857665 

2-03 

983320 

4-21 

Ol668o 

6 

55 

841116 

2-10 

867643 

2 -o 3 

983573 

4-21 

016427 

5 

54 

841247 

2 • l8 

867422 

2 -o 3 

983826 

4-21 

016174 

4 

5 ; 

841378 

2 • l8 

867800 

2 -o 3 

984079 

.. 4*21 

OIO92I 


5 i 

84 609 

2 • l8 

867178 

2 • o 3 

984331 

4-21 

OI0669 

2 

5g 

. 84;040 

2 • l8 

867066 

2 • o 3 

934584 

4-21 

016416 

1 

60 

84177 1 

2- l8 

866934 

5 -o 3 

984837 

4-21 

— 

01 5 16 3 

0 


Cosine 

D. 

Sine 

D. 

Cotang. 

D. 

Tang. 

M. 


(46 DEGREES.) 


































































I 


62 (44 DEGREES.) A TABLE OF LOGARITHMIC 


M. 

Sine 

D. 

Cosine 

D. 

Tang. 

D. 

Cotang. 


0 

9 -S 4 I 77 I 

2*18 

9-856934 

2 -o 3 

9-984837 

4-21 

io-oi 5 i 63 

60 

i 

841902 

2 • l8 

856812 

2 -o 3 

985090 

4-21 

014910 

$9 

2 

842 o 33 

2 • 18 

866690 

2 • 04 

985343 

4-21 

014657 

58 

3 

842 i 63 

2-17 

856568 

2 -04 

985596 

4-21 

014404 

67 

4 

842294 

2 • 17 

856446 

2 -04 

986848 

4-21 

oi 4 i 52 

56 

5 

842424 

2-17 

856323 

2 • 04 

986101 

4-21 

013899 

55 

6 

842555 

2-17 

856201 

2 • 04 

9S6354 

4-21 

013646 

54 

7 

842685 

2-17 

866078 

2-04 

986607 

4-21 

013393 

53 

8 

842815 

2-17 

855956 

2 • 04 

986860 

4-21 

oi 3 i 4 o 

52 

9 

842946 

2-17 

855833 

2-04 

987112 

4-21 

012888 

5 i 

IO 

843076 

2-17 

855711 

2 • o 5 

987365 

4-21 

012635 

5 o 

11 

9-843206 

2- l6 

9-855588 

2 -o 5 

9-987618 

4-21 

10-012382 

49 

12 

843336 

2 • l6 

855465 

2 -o 5 

987871 

4-21 

012129 

48 

i 3 

843466 

2 • l6 

855342 

2 -o 5 

9881 23 

4-21 

011877 

47 

i 4 

843695 

2- l6 

855219 

2 • o 5 

988376 

4-21 

011624 

46 

i 5 

843726 

2 • l6 

860096 

2 ■ o 5 

988629 

4-21 

011371 

45 

16 

843855 

2 • l6 

854973 

2-05 

988882 

4-21 

011118 

44 

17 

843984 

2 • l6 

85485 o 

2 -o 5 

989134 

4-21 

010866 

43 

10 

844114 

2- l 5 

854727 

2 -06 

989387 

4-21 

oio 6 i 3 

42 

19 

844243 

2 • I 5 

8546 o 3 

2-06 

989640 

4-21 

oio 36 o 

4 i 

20 

844372 

2 • I 5 

854480 

2-06 

989893 

4-21 

010107 

4 o 

21 

9-844602 

2 • 15 

9-854356 

2-06 

9-990146 

4-21 

10-009855 

39 

22 

84463 1 

2 • I 5 

854233 

2 • 06 

990398 

4-21 

009602 

38 

23 

844760 

2 • 15 

854109 

2 • 06 

990601 

4-21 

009349 

37 

24 

844889 

2- l 5 

853986 

2 • 06 

990903 

4-21 

009097 

36 

25 

846018 

2 * 15 

853862 

2 • 06 

991166 

4-21 

008844 

35 

26 

845 i 47 

2 • I 5 

853738 

2 • 06 

991409 

4-21 

008691 

34 

27 

845276 

2- 14 

8536 i 4 

2-07 

991662 

4-21 

oo 8338 

33 

23 

8454 o 5 

2.14 

853490 

2-07 

991914 

4-21 

008086 

32 

29 

845533 

2-14 

853366 

2-07 

992167 

4-21 

007833 

3 i 

3 o 

84566 a 

2-14 

853242 

2-07 

992420 

4-21 

007680 

3 o 

3 i 

9-845790 

2-14 

q- 853 118 

2-07 

9-992672 

4-21 

10-007328 

29 

32 

846919 

2-14 

852994 

2-07 

992926 

4-21 

007075 

28 

33 

846047 

2- 14 

852809 

2-07 

993178 

4-21 

006822 

27 

34 

846176 

2-14 

852740 

2-07 

99343 o 

4-21 

006570 

26 

35 

846304 

2 - 14 

802620 

2-07 

993683 

4-21 

oo 63 17 

25 

36 

846432 

2 • 13 

852496 

2-08 

993936 

4-21 

006064 

24 

3 7 

84656 o 

2 • 13 

862371 

2 • 08 

994189 

4-21 

oo 58 i 1 

23 

38 

846688 

2 * 13 

862247 

2 • 08 

994441 

4-21 

oo 5559 

22 

3 9 

846816 

2- l 3 

852122 

2 • 08 

994694 

4-21 

oo 53 o 6 

21 

4 o 

846944 

2 • 13 

85 1997 

2-08 

994947 

4-21 

oooo 53 

20 

4 i 

9-847071 

2 * 13 

9-851872 

2- 08 

9-995199 

4-21 

10•004801 

1Q 

4 2 

847199 

2-13 

851747 

2-08 

996402 

4-21 

004648 

l8 

43 

847327 

2 • 13 

85 1622 

2-08 

996706 

4-21 

004295 

17 

44 

847454 

2-12 

85 1497 

2-09 

996907 

4-21 

004043 

l6 

45 

847582 

2-12 

85 1372 

2-09 

996210 

4-21 

003790 

i 5 

46 

847709 

2-12 

85 1246 

2-09 

996463 

4-21 

oo 3537 

14 

47 

847836 

2-12 

85 1121 

2-09 

99671 5 

4-21 

oo 3285 

i 3 

48 

847964 

2-12 

850996 

2-09 

996968 

4-21 

oo 3 o 32 

12 

49 

848091 

2-12 

860870 

2-09 

997221 

4-21 

002779 

11 

5 o 

848218 

2-12 

850745 

2-09 

997473 

4-21 

002627 

10 

5 i 

9 • 848345 

2-12 

9 - 85 o 6 i 9 

2-09 

9-997726 

4-21 

10-002274 

9 

52 

848472 

2 - II 

86049) 

2-10 

997979 

4-21 

002021 

8 

53 

848899 

2 • 11 

85 o 368 

2-10 

998231 

4-21 

001769 

7 

54 

848726 

2 • 11 

850242 

2-10 

998484 

4-21 

ooi 5 i 6 

6 

55 

848852 

2-11 

85 oi16 

2-10 

998737 

4-21 

001263 

5 

56 

848979 

2 • 11 

849990 

2 • 10 

998989 

4-21 

001011 

4 

57 

849 1 06 

2- I I 

849864 

2-10 

999242 

4-21 

000768 

3 

58 

849232 

2 • 11 

849738 

2-10 

999496 

4-21 

ooo 5 o 5 

2 

59 

849309 

2-1 I 

8496 11 

2-10 

999748 

4-21 

000253 

1 

60 

84948a 

2 • 11 

849485 

2 • 10 

10-000000 

4-21 

1 

10-000000 

0 


! Cosine 

D. 

Sine 

! D. 

! Cotang. 

1 

D. 

Tana:. 

. 1-- - - 

! M. 


(45 DEGREES.) 





























































A TABLE OF NATURAL SINES. 


63 


M 

0 Deg. 

1 Deg. 

2 Deg. 

3 Deg. 

4 Deg. 

M 

S. 

C. 8. 

S. 

(J. S. 

s. 

0. S. 

S. 

C. S. 

S. 

C. S. 

0 

00000 

Unit. 

01745 

99985 

03490 

99939 

o 5234 

99863 

06976 

99756 

60 

i 

00029 

I*0000 

01774 

99984 

03319 

99938 

o 5263 

99861 

07005 

99764 

5 o 

2 

ooo 58 

I-0000 

oi 8 o 3 

99984 

o 3548 

99937 

o 52 g 2 

99860 

07034 

99762 

58 

3 

00087 

I-0000 

oi 832 

99988 

03577 

99936 

o 532 i 

99858 

07063 

99760 

57 

4 

00116 

I-0000 

01862 

99983 

o 36 o 6 

99935 

o 535 o 

99857 

07092 

99748 

56 

5 

00145 

I-0000 

01891 

99982 

o 3635 

99984 

05379 

99855 

07121 

99746 

55 ! 

6 

00175 

I*0000 

01920 

99982 

o 3664 

99933 

o 54 o 8 

99854 

07150 

99744 

54 : 

7 

00204 

1 • 0000. 

01949 

99981 

03693 

qqq 32 

06437 

99852 

07179 

99742 

53 ! 

8 

00233 

I-oooo 

01978 

99980 

03723 

99981 

06466 

99851 

07208 

9974 o 

52 ! 

9 

00262 

1.0000 

} 02007 

99980 

08752 

99980 

06496 

99849 

1 07237 

99738 

5 ij 

IO 

00291 

1.0000 

02036 

99979 

03781 

99929 

O0624 

99847 

07266 

99736 

5 o 

11 

00320 

99999 

02065 

99979 

o 38 io 

99927 

o 5553 

99846 

0729O 

99734 

4 , 

12 

00349 

99999 

02094 

99978 

08889 

99926 

00682 

99844 

07824 

99731 

48 

i 3 

00378 

99999 

02123 

99977 

08868 

99925 

o 56 11 

99842 

07353 

99729 

47 | 

U 

00407 

99999 

021 52 

99977 

08897 

99924 

06640 

99841 

07382 

99727 

46 i 

i 5 

00436 

99999 

02181 

99976 

03926 

99923 

! 06669 

99889 

07411 

99725 

45 1 

16 

00465 

99999 

02211 

99976 

o 3 g 55 

99922 

06698 

9 9 838 

07440 

99723 

44 1 

17 

00495 

99999 

02240 

9997D 

03984 

99921 

06727 

9 9 836 

07469 

99721 

43 ! 

18 

oo524 

99999 

02269 

99974 

0401 3 

99919 

06756 

99834 

07498 

99719 

42 ! 

19 

oo 553 

99998 

02298 

99974 

04042 

99918 

06780 

99833 

07627 

99716 

41 

20 

oo582 

99998 

02327 

99973 

04071 

99917 

06814 

99831 

07556 

99714 

40 

21 

00611 

99998 

02356 

99972 

04100 

99916 

06844 

99829 

07685 

99712 

391 

22 

00640 

99998 

02385 

99972 

04129 

999 15 

05873 

99827 

07614 

99710 

38 

23 

00669 

99998 

02414 

99971 

o 4 i 5 o 

99913 

06902 

99826 

07643 

99708 

37 

24 

00698 

99998 

02443 

99970 

04188 

99912 

oOg 3 i 

99824 

07672 

99706 

36 

25 

00727 

99997 

02472 

99969 

04217 

99911 

o 5 g 6 o 

99822 

07701 

997 o 3 

35 

26 

00766 

99997 

02501 

99969 

04246 

99910 

05989 

99821 

07780 

99701 

341 

27 

00786 

99997 

o 253 o 

99968 

04275 

99909 

06018 

99819 

07769 

99699 

33 

28 

00814 

99997 

o 256 o 

99967 

o 43 o 4 

99907 

06047 

99817 

07788 

996 q 6 

32 

29 

00844 

99996 

02689 

99966 

04333 

99906 

06076 

9981.5 

07817 

99^4 

3 i 

3 o 

00873 

99996 

02618 

99966 

04362 

99905 

06106 

99813 

07846 

99692 

3 o 

3 1 

00902 

99996 

02647 

99965 

04391 

99904 

061 34 

99812 

07875 

99689 

29 

32 

00931 

99996 

02676 

99964 

04420 

99902 

061 63 

99810;, 

07904 

99687 

28! 

33 

00960 

99990 

02705 

99963 

04449 

99901 

06192 

99808 

07933 

99680 

27 1 

34 

00989 

99995 

02734 

99968! 

04478 

99900 

06221 

99806 

07962 

99683 

26 

35 

01018 

99990 

02763 

qqq62| 

04507 

99898 

062 5 o 

99804 

07991 

99600 

25 

36 

01047 

99995 

02792 

99961; 

04686 

99897 

06279 

99803 

08020 

99678 

24 

37 

01076 

99994 

02821 

00060! 

04565 

99896 

o 63 o 8 

99801 

08049 

99676 

23 1 

38 

01 io 5 

99994 

02800 

99959 

04694 

99894 

o 6337 

99799 

08078 

99673 

22 j 

3 9 

011 34 

99994 

02879 

99959 

04623 

99893 

o 6366 

99797 

08107 

99671 

21 j 

40 

01164 

99993 

02908 

99958 

04653 

99892 

06396 

99795 

081 36 

99668 

20 1 

41 

01193 

999981 

02938 

99907 

04682 

99890 

06424 

99793 

081 65 

99666 

*9 j 

42 

01222 

99993 

02967 

99906 

04711 

99889 

06453 

99792 

08194 

99664 

18! 

43 

OI 25 l 

99992 

02996 

90000 

04740 

99888 

06482 

99700 

08223 

99661 

*7 

44 

01280 

99992 

o 3 o 25 

999-04 

04769 

99886 

06011 

99788 

08202 

99669 

u 

45 

01309 

99991 

o 3 o 54 

99953 

04798 

99886 

06640 

99786 

08281 

99657 

10 5 

46 

oi 338 

99991 

o 3 o 83 

OOo 52 

04827 

99883 

06669 

99784 

o 83 10 

99654 

14 1 

47 

01367 

9999 1 

o 3 i 12 

99952 

04856 

99882 

06598 

99782 

08339 

99662 

1 3 

43 

01396 

9999 ° 

o 3 i 4 i 

99951 

04885 

99881 

06627 

99780 

o 8368 

99649 

12 1 

49 

01426 

99990 

03170 

99900 

04914 

99879 

o 6656 

99778 

08397 

99647 

11 

5 o 

01454 

99,89 

03199 

99949 

04943 

99878 

06680 

99776 

08426 

99644 

10 

5 i 

01483 

99989 

03228 

99948 

04972 

99876 

06714 

99774 

o 8455 

99642 

9 

52 

oi 5 i 3 

99989! 

08267 

99947 

o 5 ooi 

99870 

06743 

99772 

08484 

99639 

8 

53 

01 5/*2 

qoqBS 

03286 

99946 

o 5 o 3 o 

99873 

06773 

99770 

oS 5 i 3 

99637 

7 

54 

01571 

99988 

o 33 i 6 

99945 

o 5 o 59 

99872 

06802 

99768 

08042 

99635 

6 

55 

01600 

999871 

03345 

99944 

o 5 o 88 

99870 

o 6 S 3 1 

99766 

08071 

99682 

5 

56 

01629 

99987 

03374 

99943 

o 5 i 17 

99S69 

06860 

99764 

08600 

99 63 0 

4 

57 

01 658 

99986; 

o 34 o 3 

99942 

o 5 i 46 

99867 

06889 

99762 

08629 

99627 

4 

v> 

58 

01687 

99986 

o 3432 

99941 

o 5 i 75 

99866 

06918 

99760 

o 8658 

996 2 5 

2 

59 

01716 

99980 

o 346 i 

99940 

o 52 o 5 

99864 

06947 

99708 

08687 

99622 

1 

M 

C. S. ! S. 

C. S. 

s. 

C. S. 

S. 

0.8. 


0 . S. 

8. 

M 


89 Deg. I 

88 Deg. 

87 Deg. 

80 Deg. 

85 Deg. 































































































64 


A TABLE OF NATURAL SINES. 



5 Deg. 

6 Deg. 

7 Deg. 

8 Deg. 

9 Deg. 


M 

S. 

| 0 . S. 

S. 

0. s. 

S. 

! c. s. 

S. 

C. S. 

S. 

| 0 S. 

M 

0 

08716 

99619 

io 45 c 

99452 

12187 

| 99255 

13917 

99027 

1564c 

98769 

60 

i 

08745 

00617 

10482 

99449 

12216 

99251 

13946 

99023 

15672 

! 98764 

69 

2 

08774 

99614 

io 5 i 1 

99446 

12245 

99 2 48 

13975 

99019 

15701 

98760 

58 

3 

o 88 b 3 

99612 

10 54 o 

99443 

12274 

1 99 2 44 

14004 

99015 

15730 

98755 

57 

4 

o 883 i 

99609 

io 56 g 

99440 

12302 

1 99240 

i 4 o 33 

99011 

15768 

9S751 
98746 

56 

5 

08860 

99607 

10597 

99437 

12331 

99237 

14061 

99006 

15787 

55 

6 

08889 

99604 

10626 

99434 

12360 

99238 

14090 

99002 

1 58 16 

98741 

54 

7 

08918 

99602 

io 655 

9943 1 

12389 

99230 

14119 

98908 

15845 

98737 

53 

8 

08947 

99699 

10684 

99428 

12418 

99226 

14148 

98994 

15873 

98732 

52 

9 

08976 

99596 

10713 

99424 

12447 

99222 

14177 

98990 

15902 

1 98728 

5 i 

IO 

09005 

99094 

10742 

99421 

12476 

99219 

99215 

i 42 o 5 

98986 

159311 98728 
15959 98718 

5 o 

11 

09034 

ft 

10771 

99418 

i 25 o 4 

14234 

98982 

49 

12 

09063 

10800 

994 i 5 

12533 

99211 

14263 

98978 

169881 98714 

16017 98709 
16046) 98704 

48 

i 3 

09092 

99686 

10829 

io 858 

99412 

99409 

12562 

99208 

14292 

98973 

47 

14 

09121 

99583 

12591 

99204 

14320 

98969 

98965 

46 

i 5 

09150 

99580 

10887 

99406 

12620 

99200 

14349 

1.6074 

! 98700 

45 

16 

09179 

09208 

99 5 7 8 

10916 

99402 

12649 

99197 

14378 

98961 

i 6 io 3 

98695 

44 

*7 

99575 

10945 

99399 

12678 

99103 

14407 

98957 

161 3 2 

98690 

43 

18 

09237 

99572 

10973 

99396 

12706 

99189 

14436 

98953 

16160 

98686 

42 

i 9 

09266 

99570 

11002 

99393 

i 2 7 35 

99186 

14464 

98948 

98944 

16189 

98681 

4 i 

20 

09296 

99067 

iio 3 i 

99390 

99386 

12764 

99182 

14493 

16218 

98676 

4 o 

21 

09324 

09353 

99564 

11060 

12793 

99 H 8 

14622 

98940 

16246 

98671 

3 9 

22 

99562 

11089 

99383 

12822 

99*76 

1 455 1 

98986 

16276 

98667 

38 

23 

09382 

99 55 9 

11118 

99380 

1 285 1 

99171 

14580 

98931 

1 63 04 

98662 

37 

24 

09411 

99606 

11147 

11176 

99377 

12880 

99167 

14608 

98927 

i 6333 

98657 

36 

25 

09440 

99553 

99374 

12908 

99163 

14637 

q 8 q 23 

i 636 i 

98652 

35 

26 

09460 

09498 

9955 i 

I 1205 

99370 

I2 9?7 

99160 

14666 

98919 

16390 

98648 

34 

27 

99548 

11234 

99 36 7 

12966 

991 56 

14695 

98914 

16419 

98643 

33 

28 

09527 

99545 

11263 

99364 

12995 

99152 

14723 

98910 

16447 

9 8638 

32 

29 

09556 

99542 

11291 

99360 

i 3 o 24 

99148 

U 752 , 

98906 

16476 

98633 

3 i 

3 o 

09585 

99540 

11320 

99357 

i 3 o 53 

99144 

14781 

98902 

i 65 oo 

9S629 

3 o 

3 i 

09614 

99537 

11349 

11378 

99354 

i3o8i 

99141 

14810 

98897 

16533 

98624 

29 

32 

09642 

99534 

9935 i 

1 3 110 

99137 

1 4838 

98893 

16062 

98619 

28 

33 

09671 

9953 i 

11407 

99347 

i 3 i 3 g 

99 i 33 

14867 

98889 

16691 

9S614 

27 

34 

09700 

99528 

1 1436 

99 3 44 

1 3 168 

99129 

99125 

14896; 

98884 

16620 

98609 

26 

35 

09729 

09758 

99526 

1 1465 

99341 

1 3 197 

14925 

98880 

16648 

98604 

25 

35 

99523 

11494 

99337 

13226 

99122 

14954 

98876 

16677 

98600 

24 

37 

09787 

99520 

11 523 

99334 

13254 

99118 

14982 

1 5 o11' 

98871 

16706 

98595 

23 

38 

09816 

99517 

11 552 

9933 i 

13283 

99114 

98867 

16734 

98690 

22 

3 9 

09845 

99514 

1 i 58 o 

99327 

99324 

1 331 2 

99110 

i 5 o 4 o 

98863 ] 

16763 

98585 

21 

40 

09874 

09903 

99511 

11609 

1 334 1 

99106 

i 5 o 69 ! 

9 S 85 S| 

16792 

98580 

2q 

4 i 

99508 

11 638 

99320 

13370 

99102 

15097: 

9 8854 

16820 

98575 

19 

42 

09982 

99506 

11667 

99317 

13399 

99098 

10126; 

98849 

16849 

98570 

18 

43 

09961 

995 o 3 

11696 

9 ^ 3 1 4 

13427 

99094 

1 5 i 55 

98845! 

16878 

9 S 565 

17 

44 

45 

09990 

10019 

99000 

99497 

11726 

11754 

99310 

99307 

13456 

13485 

99091 

99087 

1 5 184 

152 12 1 

98841 

9 8336 

16906 

16935 

98561 

98556 

16 

16 

46 

10048 

99494 

11783 

9g3o3 

i 35 i 4 

99083 

1 5241 

98882 

16964 

9855 i 

14 

47 

48 

I00 77 

10106 

99491 

99488 

11812 

11S40 

99300 

99297 

13543 

13572 

99079 

99075 

16270' 

15292 

98827] 

98823! 

16992 

17021 

98546 

98541 

i 3 

12 

i 9 

101 35 

99485 

11869 

11898 

99293 

i 36 oo 

99071 

15327 

98818! 

I 7 o 5 o 

98536 

11 

5 o 

10164 

99482 

99290 

99286 

18629 

99067 

15356 

98814] 

17078 

9 853 1 

10 

5 i 

10192 

99479 

99476! 

11927! 

i 3658 

99063 

1 5385 ; 

98809 

17107 

98526 

9 

52 

10221 

1 ig 56 

99283 

13687 

99059 

i 54 i 4 | 

98800! 

17136 

98621 

8 

53 

I 025 o 

994731 

119851 

99279 

13716 

99055| 

1 54421 

98800 

17164 

98516 

7 

54 

10279 

99470 

12014] 

99276 

13744 

99001! 

i 547 L 

98796 

17193 

98511 

6 

55 

io 3 o 8 | 

99467! 

12043 

99272 

13773 

99047 

i 55 ooj 

ft 

17222 

98506 

5 

56 

1o 337 j 

99464 

12071| 

99269 

13802! 

99043 

15529 

17200 

98501 

4 


io 366 

99461 

12100 

99265 

1 383 1 1 

99039! 

i 5557 

98782] 

17279 

98496 

3 

58 

5 9 

10395 

99458 

12129 

99262 

i 3 S 6 o 

9903 5 1 

1 5586 

98778 

17308 

98491 

2 

10424 

99455 

12 158 

99208 

13S89 

99031 

1 56 1 5 

98773 : 

17336 

98486 

1 

m 

C. S. 

S. 

C. S. ! 

S. 

0 . S. 1 

S. 

0 . S. 

s. 1 

C. S. 

S. 



84 Deg. 

83 Deg. 

82 Deg. j 

81 Deg. 

80 Deg 













































































































A TABLE OF NATURAL SINES. 


65 


M 

10 Deg. 

11 Deg. 

12 Deg. 

13 Deg. 

14 Deg. 

S. 

C. S. 

S. 

C. S. 

S. 

0 . S. 

S. 

22496 

22623 

22552 

22580 

22608 

22637 

22665 

22693 

22722 

22760 

22778 

22807 

22835 

22863 

22S92 

22920 

22948 
22977 
23 oo 5 
23 o 33 
23062 
23090 
23 1 18 
23146 
23175 

23203 
23231 
23260 
23288 
2 . 33 16 
23340 

23373 

23401 

23429 

23458 

23486 

235 i 4 

23542 

23571 

23599 

23627 

23656 

23684 

23712 

23740 

23769 

23797 

2.3825 

2.3853 

2'3882 

2.8910 

23938, 

23966 

2,3995 

24023 

24 o 5 i 

24079 
24108 
241 36 
24164 

c. s. 

97437 
9743 o 
97424 
97417 
974 n 
97404 
97898 
97391 
97.384 
97378 
97371 

97365 

97358 

9735 , 

97.345 

97338 

9733 i 

97325 

973 i 8 

973 h 

973 o 4 

97298 

97291 

97284 

97278 

97271 

97264 

97257 

97251 

97244 

97237 

9723 o 

9722,3 

97217 

97210 

97203 

97196 

97189 

97182 

97176 

97169 

97162 

97160 

97*48 

97 * 4 i 

97*34 

97127 

97120 

97113 

97106 

97100 

97003 

97086 

97079 

97072 

97065 

97058 

97 o 5 i 

97044 

97037 

S. 

24192 
24220 
24249 
24277 
243 o 5 
24333 
24362 
24390 
24418 
24446 
24474 
245 o 3 
24.53 1 
24559 
24587 
24616 

24644 

24672 

24700 

24728 

24766 

24784 

248 i 3 

24841 

24869 

24897 

24925 

24953 

24982 

25 oio 

25 o 38 

2 5 066 
25094 
26122 
25 1 5 1 

25 1 79 

26207 

25235 

26263 

25291 

25320 

2.5348 

20376 

26404 

264,32 

2546b 

20488 
255 16 
25545 

25573 

256 oi 

26629 

25657 

25685 

26713 

26741 

26769 

26798 

25826 

25854 

C. S. 

97080 

97023 

97016 

97008 

97001 

96904 

96987 

96980 

96973 

96966 

96909 

96902! 

96940 

96987 

969.30 

96923 

96916 

96909 

96902 

96894 

96887 

96880 
96S73 
96866 
9 6858 

96881 
96844 
96837 
96829 
96822 
96815 

96807 

96800 

96793 

96786 

96778 

96771 

96764 

96766 

96749 

96742 

96734 

96727 

96719 

96712 

96705 

96697 

96690 

96682 

96676 

96667 

96660 

9 6653 

96645 

96638 

96630 

9662.3 

96616 

96608 

96600 

0 

1 

2 

3 

4 

5 

6 

9 

10 

11 

12 

1 3 

1 4 

1 5 

16 

\l 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 

35 

36 

37 

38 

39 

3 o 

41 

42 

43 

44 

45 

46 

47 

48 

n 

5 1 

52 

53 

54 

55 

56 

57 

58 

5 9 

17365 

17393 

17422 

i 745 i 

17479 

17508 

17537 

17565 

17594 

17623 

17651 

17680 

17708 

j 7737 

17766 

17794 

17823 

17862 

17880 

1 79°9 

17937 

17966 

17995 

18023 

i 8 o 52 

1S081 

18109 

i 8 i 38 

18166 

i 8 i 9 5 

18224 

18252 
18281 
1 83 09 
i 8338 
18367 
i 83 9 5 
18424 
18462 
18481 
18509 
1 8538 
18567 
18695 
18624 
18652 

1 868 1 
18710 
18738 

1 8767 

Ill^l 

1 8852 

18881 

18910! 

18938 

18967' 

18995 

19024 

19052 

98481 

98476 

98471 

98466 

98461 

98455 

98450 

98445 

98440 

98435 

98430 

98425 

98420 

98414 

98409 

98404 

9 83 99 

98394 

98389 

98383 

98378 

983 7 3 

98368 

98362 

98357 

9 835 2 

98347 

98341 

98336 

9833 i 

98325 

98320 
983 1 5 
98310 

98304 

98299 

98294 

98288 

98283 

98277 

98272 

98267 

98261 

98266 

98250 

98245 

98240 

98234 

98229 
9822.3 
9S218 
98212 
98207! 
98201! 
98196 
98190 

98185 

98179 

98174 

98168 

19081 

19109 

19138 

19167 

19198 

19224 

19262 

19281 

19309 

u ;338 

19366 

19.395 

19423 

19452 

19481 

19509 

19538 

19866 

19695 

19623 

19662 

196S0 

19709 

1 97^7 
19766 

*9794 

19823 

19861 

19880 

19908 

19937 

19965 

19994 

20022 

2 oo 5 i 

20079 

20108 

2 oi 36 

2 oi 65 

20193 

20222 

20260 

20279 

20307 

2 o 336 

2 o 364 

20393 

20421 

20460 

20478 

20807 

2 o 535 

2 o 563 

20592 

20620 

20640 

20677! 

20706 

207.34 

20763 

98163 

98157 

98162 

98146 

98140 

98135 

98129 

98124 

98118 
98112 
98107 
98101 
98096 
98090 

98084 

98079 

98073 

98067 

98061 

98056 

98060 

98044 

98039 

98033 

98027 

98021 

98016 

98010 

98004 

97998 

97992 

97987 

97981 

97975 

97969 

9790 3 

9795 8 

97902 

97946 

97940 

979 3 4 

97928 

97922 

979 l6 

97910 

97 9 °5 

97899 

97893 

97887 

97881 

97875 

97869 

97.863 

97867 

97861 

97845 

97339 

97833 

97827; 

97821 

20791 

20820 

20848 

20877 

20905 

20933 

20962 

20990 

21019 

21047 

21076 
21104 

21 132 
21 l6l 
21189 
21218 

21246 
21275 
2 i 3 o 3 
2 133 1 
2 i 36 o 
21 388 

.21417 

21445 
21474 
21 5 o 2 
2 i 53 o 
21059 
21587 
21616 

21644 

21672 

21701 

21729 

21768 

21786 

21814 
21 843 
21871 
21890 
21928 
21966 
21985 
220 l 3 
2 2041 
2207O 

22098 

22126 

22 l 55 

2218.3 

22212 

22240 

22268 

22297 

22325 

22353 

2 2382 
22410 
22438 
22467 

97815 

97809 

9780.3 

97797 

9779 ’ 

97784 

97778 

97772 

97766 

9776 o 

97754 

97748 

97742 

97730 

97729 

97723 

977 H 

97711 

97705 

97698 

97602 

97686 

97680 

97673 

97667 

97661 

97655 

97648 

97642 

97636 

97630 

97623 

97617 
97611 

97604 

97598 
97592 
97585 
97579 
97073 
97566 
97660 
97553 
97547 
97541 
97534 
97028 
9752 ! 
975 l 5 
975 o 8 
97602 
97496 
97489 
97483 
97476 
97470 
97463 
97457 
97460 

97444 

M 

C. S. 

~s: 

C. s. 1 

S. 

0. s. 1 

X. 

C. S. 

S. 

c. s. 1 s. 

79 Deg. 

78 Deg. 

77 Deg. 

76 Deg. 

75 Deg. 


M 

6oi 

5 9 

58 

D7 

56 

55 

54 

53 

52 

5 i 

5 o 

49 1 

48 ! 

4 2l 

401 

45 


43 

42 

41 

40 

3 ? 

37 

36 

35 

34 

33 

32 

3*1 

3 oj 

29' 
28 
27 I 
26| 
25 ) 
24 1 
23 
22 
21 
20 
19 
18 
17 
[6 
i 5 

14 

i 3 
12 
11 
10 i 


7 
6 
5 
4 
3 
2 ! 
I I 
M 







































































































66 


A TABLE OF NATURAL SINES. 



15 Deg. 

16 Deg. 

17 Deg. 

18 Deg. 

19 Deg. 


M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

S.C. 

M 

0 

26882 

96693 

27564 

96126 

29237 

9563o 

30902 

96106 

32557 

94552 

60 

i 

26910 

9 6585 

27692 

96118 

29265 

96622 

30929 

96097 

32684 

94542 

69 

2 

25938 

96578 

27620 

96110! 

29293 

956i3 

30957 

95088 1 

32612 

94533 

58 

3 

25g66 

96570 

27648 

96102 

29321 

g56o5 

30986 

95079 

32639 


57 

4 

20994 

96562 

27676 

06094 

29348 

96696 

31012 

96070 

32667 

94614 

56 

5 

26022 

96555 

27704 

96086 

29376 

(25588 

31040 

95061 

32694 

94604 

55! 

6 

26060 

96547 

27731 

96078 

29404 

96679' 

31068 

95o52| 

32722 

94495 

64 

7 

26079 

96540 

27759 

96070 

29432 

95571 

31095 

95o43 

32749 

9 44«5 

53 

8 

26107 

96532 

27787 

96062; 

29460 

95562; 

3ii23 

g5o33 

32777 

94476 

62 

g 

26i35 

96524 

27815 

96054 

29487 

95554 

31151 

95024 

32804 

94466 

61 

10 

26i63 

96617 

27843 

96046 

29515 

95545 

31178 

g5oi5 

32832 

94457 

5o 

11 

26191 

96509 

27871 

96087 

29543 

95536 

3i 206 

96006; 

328591 

94447 

49 

12 

26219 

96602 

27899 

96029 

29671 

95528 

31233 

94997) 

32887 

94436 

48 

i3 

26247 

96494 

27927 

96021j 

29% 

95519 

31261 

94988 

32914 

94428 

47 

14 

26275 

96486 

27955 

96013 

29626 

95511 

31289 

94979! 

32942 

94418 

46 

i5 

263o3 

96479 

27983 

96005 

29654 

96602 

3i3i6 

94970 

32969 

94409 

45 

16 

26331 

96471 

28011 

96997j 

29682 

95493! 

3i344 

949611 

32997 

94399 

44 

17 

26359 

96463 

28039 

95989 

29710 

95485 

31372 

94952 

33o24; 

94890 

43 

18 

26387 

96406 

28067 

96981 

29737 

95476’ 

31899 

94943 

33o5i 

94360 

42 

19 

26416 

96448 

28096 

95972 

29765 

95467 

31427 

94933 

33o79| 

94370 

4i 

1 20 

26443 

g6440 

28123 

95964 

29793 

96459 

31454 

94924, 

331 ob 

9436i 

4o 

21 

26471 

96433 

28i5o 

g5g56 

29821 

g545o 

3i482 

94916 

33134 

943oi 

3 9 

22 

265oo 

96425 

28178 

95948 

29849 

9544i 

3i5io 

94906, 

33161 

94342 

36 

23 

26628 

96417 

28206 

g5g4o 

29876 

95433 

3 i537 

94897' 

33189 

94332 

37 

24 

26556 

96410 

28234 

g5g3i 

29904 

95424 

31565 

94888 

33210 

94322 

36 

25 

26584 

96402 

28262 

95923 

29932 

9 54i5 

315g3 

94878 

33244 

g43i 3 

35 

26 

26612 

96394 

28290 

95916 

29960 

95407 

31620 

94869 

33271 

94808 

34 

27 

26640 

g6386 

28318 

959 0 7 

29987 

95398 

31648 

94860 

33298 

94293 

33 

28 

26668 

9 63 79 

28346 

95898 

3ooi5 

95389 

31675 

94861 

33326 

94284 

32 

29 

26696 

96371 

28374 

95890 

30043 

9538o 

31703 

94842 

33353 

94274 

3i 

3o 

26724 

9 6363 

28402 

9 5882 

30071 

95372 

31730 

94832 

3338i 

94264 

3o 

3i 

26752 

96355 

28429 

95874 

30098 

9 5363 

31758 

94823 

33408 

94254 

2 9 

32 

26780 

96347 

28467 

g5865 

30126 

95354 

31786 

94814 

33436 

94245 

28 

33 

26808 

96340 

28485 

90857! 

30164 

95345 

318i 3 

948o5 

33463 

94235 

27 

34 

26836 

96332 

28513 

95849 

30182 

95337 

31841 

94795 

33490 

94226 

26 

35 

26864 

96324 

28541 

g584i 

30209 

95328 

31868 

94786 

335i8 

942i5 

26 

36 

26892 

g63i6 

28669 

9 5832 

30237 

95319 

81896 

94777 

33545 

94206 

24 

37 

26920 

g63o8 

28597 

95824 

30265 

g5310 

31923 

94768 

33573 

94196 

23 

38 

26948 

96301 

28625 

9 58i6 

30292 

953oi 

31 g51 

94758 

336oo 

94166 

22 

39 

26976 

96293 

28662 

95807 

3o32o 

95293 

3 1979 

94749 

33627 

94176 

21 

40 

27004 

96285 

28680 

95799 

3o348 

96284 

32006 

94740 

33655 

94167 

20 

4i 

27032 

96277 

28708 

96791 

30376 

96275 

32o34 

9473o 

33682 

94157 

IO 

42 

27060 

96269 

28736 

90782 

3o4o3 

96266 

32061 

94721 

33710 

94147 

l8 

43 

27088 

96261 

28764 

95774 

3o43 1 

95257 

320S9 

94712 

33737 

94i37 

17 

44 

27116 

96263 

28792 

9 5 7 66 

30459 

96248 

32116 

94702 

33764 

94127 

l6 

45 

27144 

96246 

28820 

96757 

30486 

95240 

32144 

94693 

33792 

94118 

i5 

46 

27172 

96238 

28847 

95749 

3o5i4 

96231 

32171 

94684 

33819 

94108 

14 

47 

27200 

96230 

28875 

95740 

3o542 

96222 

32199 

94674 

33846 

94098 

i3 

48 

27228 

96222 

28903 

95782 

30670 

96213 

32227 

94665 

33874 

94068 

12 

49 

27256 

96214 

28931 

96724 

30597 

90204 

32254 

94656 

33901 

■94078 

11 

5o 

27284 

96206 

28959 

95715 

3o625 

95195 

32282 

94646 

33929 

94068 

10 

5i 

27312 

96198 

28987 95707 

3o653 

95186 

32809 

94637 

33956 

9 4o58 

9 

52 

27340 

96190 

29016 

95698 

3o68o 

95177 

32337 

94627 

33 9 83 

94049 

6 

53 

27368 

96182 

29042 

95690 

30708 

96168 

32364 

94618 

34oi 1 

9 4o3g 7 

54 

27396 

96174 

29070 

9568i 

30736 

95 1 69 

32392 

94609 

34o38 

94029 6 

55 

27424 

96166 

29098 

95673 

30763 

96160 

32419 

94699 

3 406 5 

94019 

5 

56 

27452 

96158 

29126 

g5664 

30791 

95142 

32447 

94690 

34093 

94009 

4 

57 

27480 

96150 

29164 

95656 

30819 

9D133 

32474 

94680 

34120 

9 3 99 9 

3 

58 

27508 

96142 

29182 

g5647 

30846I g5124 

32502 

94571 

34i47 

o3o6g 

2 

5g 

27536 

96134 

29209 

96639 

30874 g5115 

32529 

9456i 

34176 

93979 

1 

M 

C. S. 

S. 

C. S. 

S. 

C. S. 

1 s. 

C. S. 

S. 

C. S. 

i S. 

M 


74 Deg. 

73 Deg. 

72 Deg. 

71 Deg. 

70 Deg. 

J 





















































































A TABLE OF NATURAL SINES. 


67 



20 

Deg. 

M 

S. 

C. S. 

0 

3420: 

93969 

1 

3422c 

? 96969 j 

2 

3425 ' 

93949 

3 

3428/ 

u93939 

4 

343 1 

q 3 o 2 q 

5 

3433 c 

93919 

6 

3436 d 

q 3 qoq 

7 

3489^ 

93899 

0 

34421 

98889 

9 

3444 £ 

98879 

10 

34475 

98869 

11 

345 o 3 

c ;3859 

12 

3453 c 

98849 

i 3 

34557 

98839 

i 4 

34584 

98829 

i 5 

34612 

98819 

16 

34639 

93809 

17 

34666 

9 3 799 

18 

34694 

93789 

19 

34721 

9 3 779 

20 

34748 

9 3 769 

21 

3477 5 

93769 

22 

348 o 3 

9 3 748 

23 

3483 o 

93738 

24 

34857 

93728 

25 

34884 

93718 

26 

34912 

93708 

27 

34939 

98698 

28 

34966 

9 3688 

29 

34998 

9 3 677 

3 o 

35o2i 

93667 

3 i 

35 o 48 

93657 

32 

35 o 75 

98647 

33 

35 io 2 

93637 

34 

35 i 3 o 

93626 

35 

35 167 

93616 

36 

35 i 83 

93606 

37 

352 ii 

93596 

38 

35239 

9 3585 

39 

36266 

93575 

40 

35293 

9 3565 

41 

35320 

93555 

42 

35347 

^3544 

43 

35375 

93534 

44 

35402 

93524 

45 

35429 

935 i 4 

46 

35456 

935 o 3 

47 

35484 

93493 

48 

355 i i 

93483 

49 

35538 

93472 

5 o 

35565 

93462 

5 i 

35592) 

93462 

52 

35619 

93441 

53 

35647 

9343 i 

54 

35674 

93420 

55 

35701 

93410 

56 

35728 

93400 

57 

35 7 55 

93389 

58 

35782 

93379 - 

69 

358 io 

93368 C 

' M 

C. S. 

S. ( 


69 Deg. 


21 Deg. 


35837 

35864 

35891 

35918 

35945 

35973 
36 ooo 
36027 
36064 
36 o 8 i 
36 io 8 
36 1 35 
36162 
36190 
36217 
36244 

36271 

36298 

36325 

36352 

36379 

36406 

36434 

36461 

36488 
365 1 5 
36542 
3 6 569 
36596 
36623 
3665 o 

36677 

36704 

36731 

36 7 58 

36785 

368 12 

36839 

36867 

36894 

36921 

36948 

36975 

37002 

37029 

37056 

37083 

37110 


C. S. 


3743.^ 


9 3358 

93348 

93337; 

93327 

93316 

93306 

93295 

93285 

93274 

93264 

93253 

93243 

93232 

93222 

93211 

93201 

93100 

93180 

93169 

93159 

93148 

93137 

93127 

93116 

93106 

93095 

93084 

93074 

93 o 63 

93o52 

93042 

93o3i 

93020 

93010 

92999 

92988 

92978 

92967 

92966 

92945 

92935 

92924 

92913 

92902 

92892 

92881 

92870 
92859 
92849 
92838 
92827 
92816 
92806 
92794 
92784 
92773 
92762 
92761 
92740 
92729 


C. S. ! S. 


68 Deg. 


22 Deg. 


S. i c. s. 


37461 92718 
37488 92707 
37515 92697 
375421 92686 
37662 9:675 
37695 92 64 
37022 92053 
37649; 92642 
37676I 92631 


37703 

37730 

37757 
377S4 
37811 
37838 
37865 

37892 

37919 

07946 

37973 

37999 

38026 

38 o 53 
38 o 8 o 
38107 
38 1 34 
38 161 
38 1S8 
382 1 5 
38241 
38268 

382 9 5 

38322 

38349 

38376 

384 o 3 

3843 o 

38456 

38483 

385 io 

38537 

38564 

38591 

38617 

38644 

38671 

38698 

38726 

38752 

38778 

388 o 5 

38832 

3885 9 

38886 

38912 

38 9 3 9 

38966 

38993 

39020 

39046 


C. S. 


92620 
92609 
92598 
92687 
92676 
92565 
92554 

92543 

92532 

92521 

92510 

92409 

92488 

92477 

92466 

92455 

92444 

92432 

92421 

92410 
92399 
92388 

92377 

92366 

92355 

92343 

92332 

92321 

92310 

92209 

92287 

92276 

92265 

92264 

92243 

9223 i 

92220 

92209 

92198 

92186 

92175 

92164 

92 l 52 

92141 
92130 
92119 
92107 
92006 
92085 
92073 
92062 


S. 


67 Deg. 


23 Deg. 

24 

Deg. 


S. 

C. S. 

S. 

I C. S. 

M 

3907 c 

92060 

40674 91355 

60 

3910c 

92039 

40700 91343 

5 o 

3 9 1 2- 

92028 

40727 

9 i 33 i 

58 

39 5 c 

92016 

40753 

91319 

57 

3918c 

92005 

4078c 

91307 

56 

3920" 

91994 

40806 

91295 

55 

3923.4 

91982 

4 o 83 ^ 

91283 

1 54 

3926c 

9 X 97 1 

4086c 

91272 

53 

39287 

91969 

40886 

91260 

52 

39314 

91948 

40913 

91248 

5 i 

39341 

91936 

40939 

91236 

5 o 

39367 

91925 

40966 

91224 

49 

89394 

91914 

40992 

91212 

48 

39421 

91902 

41019 

91200 

47 

8944^ 

91891 

41040 

91188 

46 

39474 

9 i8 79 

41072 

91176 

45 

39501 

91868 

41098 

91164 

44 

39528 

91866 

41125 

91162 

43 

3 9 555 

91845 

41 i 5 i 

91140 

42 

3 g 58 i 

9 i 833 

41178 

91128 

4 i 

89608 

91822 

41204 

91116 

4 o 

89635 

91810 

4 1 23 1 

91104 

3 9 

89661 

9H99 

41257 

91092 

38 

39688 

91787 

41284 

91080 

3 7 

39715 

9 1 775 

4 i 3 io 

91068 

36 

39741 

91764 

4^337 

91066 

35 

89768 

91762 

4 1 363 

91044 

34 

39796 

91741 

41390 

91032 

33 

39822 

91729 

41416 

01020 

32 

89848 

91718 

4 1 443 

91008 

3 i 

39875 

91706 

41469 

90996 

3o 

39902 

91694 

43496 

90984 

20 

89928 

91683 

41622 

00972 

28 

89966 

91671 

41649 

90960 

27 

89982 

91660 

41670 

90948 

26 

40008 

91648 

41602 

90936 

25 

4 oo 35 

9 i 636 

41628 

90924 

24 

40062 

91625 

41 655 

90911 

23 

4ooS8 

91613 

41681 

90899 

22 

40115 

91601 

41707 

90887 

21 

4 oi 4 i 

91690 

41734 

90875 

20 

40168 

91578 

41760 

90863 

T 

X IJ 

40195 

9 1 566 

41787 

9085 1 

18 

40221 

9 i 555 

4 181 3 

90839 

17 

402 48 

9 i 543 

41840 

90826 

16 

40275 

91 53 1 

41866 

90814 

i 5 

4 o 3 oi 

91519 

41892 

90802 

14 

40328 

9i5o8 

41919 

90790 

i3 

4 o 355 

91496 

41040 

90778 

12 

4 o 38 i 

91484 

41972 

90766 

11 

40408 

91472 

41998 

90753 

10 

40434 

91461 

42024 

90741 

9 

40461 

91449 

42061 

90729 

8 

404.88 

91437 

42077 

90717 

7 

4 o 5 i 4 

91425 

42104 

90704 

6 

40541! 

91414 

42 i 3 o 

90692 

5 

4o567 

91402 

42 1 56 

90680 

4 

40694 

91390 

42 i 83 

90668 

3 

40621 

91378 

42209 

90655 

2 

40647 

91366 

42235 

90643 

1 

H Q 

S. 

C. S. 

S. 

M 

66 Deg. 

65 Deg. 



19 


I 











































































































































68 


A TABLE OF NATURAL SINES. 


M 


o 

1 

2 

3 

4 

5 

6 

7 

8 

9 

IQ 
11 
12 

1 3 

1 4 

1 5 

16 

!2 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

3 0 

3 1 

32 

33 

34 

35 

36 
3 i 

38 

3 9 

40 

4 1 

42 

43 

44 

45 

46 

% 

49 

00 

5 1 

52 

53 

54 

55 

56 
5 
5 

J 9 

M 

I 

1 


25 Deg. 


S. ! C. S. 


42282 
42288 
423 1 5 
4234i 
42367 
42394 
42420 
42446 
42473 

42499 

42626 

42552 

42578 

42604 

4263 i 

42657 

42683 

42709 

42736 

42762 

42788 

428 i 5 

42841 

42867 

42894 

42920 

42946 

42972 

42999 

43 o 25 

43 o 5 i 

43077 

43 104 

43 i 3 o 

43 1 56 

43182 

43209 

43235 

48261 

43287 

433 1 3 ' 

4334 o 

43366 

43392 

43418 

43445 

43471 
43497 
43523 
43 549 
43575 
43602 
43628 
43654 
4368 o 
43706 
43733 
48759 
43785 
438i 1 


C. S. 


90631 

90618 

90606' 

90594 

90582 

90569 

90557 

90545 

90532 

90520 

90507 

90495 

90483 

90470 

90458 

90446 

90433 

90421 

90408 

90396 

9 o 383 

90371 

9 o 353 

90346 

90334 

90321 

90309 

90296 

90284 

90271 

90269 

90246 

90233 

90221 

90208 

90196 

90183 

90171 

90168 

90146 

9 oi 33 

90120 

90108 

90095 

90082 

90070 

90057 

90045 

90032 

90019 

00007 

89994 

89981 

89968 

89966 

89943 

89930 

89918 

8 99 o 5 

89892 


26 Deg. 


S. 


». 


64 Deg. 


43837 

43863 

43889 

43916 

43942 

43968 

43994 

44020 

44046 

44072 

44098 

44124 

44 i 5 i 

44177 

442 o 3 

44229 

44255 
44281| 
44807■ 
44333 ' 
44359 
44385 
444 i 1 
44437 
44464 

4449° 

44616 

44542 

44568 

44594 

44620 

44646 
44672 
44698 
447 2 4 
447 5o 
44776 

44802 

44828 

44854 

44880 

44906 

44932 

44968 

44984 

45oio 

45o36 
45062 
46088 
45 ii 4 
45 140 

45 166 

46192 

452 i 8 

45243 

46269 

46296 

45321 

45347 

45373 


C. S. 


27 Deg. 


S. I c. s. 


89879; 
89867 ; 

89854! 

89841 

89828I 

89816* 

89803 

89790! 

89777! 

897641 

89762! 

89739* 

89726 

89713 

89700 

89687 

89674 

89662 

89640 

89636:) 

89623;! 

89610!) 

89697 

89084 

89571 

89558 

89545 

89532 

89519 

89606 

89493 

89480 

89467 

89454 

89441 

89428 

89415 

89402 

89389 

89376 

8 9 363 

89350 

89337 

89324 

89311 

89298 

89285 

89272 

89269 

89245 

89232 

89219 

89206 

89193 

89180 

89167 

89153 

89140 

89127 

89114 


C. S. ! S. 


63 Deg. 


45399 

45420 

4545 i 

46477 

455 o 3 

455291 

45554! 

4558 o 

46606; 

45632 

45658 ; 

45684 ' 

46710, 

45736 ; 

46762 

46787! 

458 i 3 ) 
45839 ) 
46866) 
458911 

46917I 

45942! 

46968! 

46994 

46020' 

46046 

46072 

46097 

461 23 

46149 

46170 

46201 

46226 

46252 

46278 

46804 

4633 o 

46355 

46381 

46407 

46433 

46458 

46484 

46510 
46536 
4656 i 

46587 

46613 

46639 

46664 

46690 

46716 

46742 

46767 

46793 

46819 

46844 

46870 

46896 

46921 


28 Deg. 


S. 


89101 

89087 

89074 

89061) 

89048 

89035) 

89021 

89008 

88 99 5 ) 

88981 

88968 

88955[ 
88942' 
88928! 
8891s) 
88902 

88888 ) 

88875;' 

88862 

88848 

88835 ! 

8SS2 2! 

88808! 

88795 

88782 

88768, 

88 7 55 | 

88741!) 

88728' 

88716 

88701 

88688 

88674 

88661 

88647 

88634 

88620 

88607 

885 9 3 

8858 o 

88566 

88553 

88539 

88526 

885 i 2 

88499 

88485 

88472 

88458 

88445 

8843 i 

88417 

88404 

883 9 o! 

88377] 

88363 ] 

88349 

88336 

88322 

883 o 8 


c. s. 1 s. 


62 Deg. 


C. S. 


46947 

46973 

46999 

47024 

47 o 5 o 

47076 

47101 

47127 

47 i 53 

47178 

47204 

47229 

47250 

47281) 

473 o6; 

47332 

47358 

47383 ; 

47409 ! 

47434 ) 
47460) 
47486 
47611, 
47537 | 
47562 
47588 , 

47614: 

47639 1 
47660 
4769O 
47716 , 

4774 l[ 

47767, 

47793 
478 l 8 
47844 ! 
4786 
4789 

47920 | 

47946 ! 

47971 ) 

47997 

48022 

48048 

48073 ; 

48099 

48124! 

4800 

48176, 

48201) 

48226; 

48262 

48277 

483 o 3 

48328 

48354 

48379 

48406 

48430 

48466 


C. S. 


88295 

88281 

88267 

88254 

88240 

88226 

88213 ! 

88199 

88 i 85 | 

88172 

881 58 

881441 

88 i 3 o 

88117] 

88 io 3 j 

88089] 

88075!; 

88062) 

88048! 

88034 i 

88020 

88006] 

B799 3 ! 

879791 

879601 

8795 i! 

87937 

87923: 

87909] 

87896 

87882 

87868 

87854 

87840 

87826 

87812 

87798 

87784 

87770 

87756 

87743 

87729 

87715 

87701 

87687 

87673 

87669 

87640 

87631 

87617 

87603 

87689 

87575 
87661 
87546 
87532 
8 7 5 18 
87504 

87490 

87476 


29 Deg. 

M 

S. 

C. S. 

48481 

87462 

60 

485 o 6 

87448 

5 9 

| 48532 

87484 

58 


S. 


61 Deg. 


48557 

48583 

48608 

48634 

48669 

48684 

48710 

48735 

48761 

48786 

48811; 

48837 ) 

48862! 

48888! 

489 l 3 | 

48938 

48964] 

43989 

49014 

49040 

49065 

49090 

49116 

49141 

49166 

49192 

49217 

49242 

49268 

49293 

493l8j 

49344 

49369 

49394 

49419 

49445 

49470 

49495 

49621 

49646 
49571 

49696 

49622 

49647 
49672 

49697 
49723 
49748 
49773 
49793 ) 
49824) 
49849 

49874 

49899 

49924 

49960 

4997 5 

c. s. 


87420 

87406 

87391 

87377 

87363 

87349 


868 o 5 

86791 

86777 

86762 

86748 

86733 

86719 

86704 

86690 

86675 

86661 

86646; 

86632 ] 

86617] 


5? 

56 

55 

54 

53 

52 


87330 5i 
87321, 5o 
87306 49 

87292 48 

87278] 47 

87264 46 
87260 45 

87235 44 
87221 43 
87207 42 
87193 41 
87178, 40 
87164 39 
87 i 5 o 38 
871 36 j 37 
87121 36 
87107* 35 
87093 34 
87079 33 
87064) 32 
87050 3 i 
87036 3 o 

87021 29 
87007I 28 
86993 27 
86978 26 
86964 25 

86949 24 
86935 2.3 
86921 22 
86906 21 
86892 
86878 
86863 
86849 
86834 
86820 


20 

19 

18 

17 

16 

i5 


14 
i3 
12 
11 
10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

M 


60 Deg._ 





































































































A TABLE OF NATURAL SINES, 


09 



30 Leg. 

31 Deg. 

32 Deg. 

83 Deg. 

34 Deg. 


M 

S. 

C. S. 

S. 

C. S. 

S. 

C. S. 

S. 

C. S 

S. 

C. S. 

M 

0 

5 oooo 

866 o 3 

5 i 5 o 4 

86717 

52992 

84806 

54464 

8386 7 

559 IQ 

82904 

60 

i 

D 0025 

86588 

5 i 529 

86702 

53017 

84789 

54488 

8385 1 

55943 

82887 

5 9 

2 

5 oo 5 o 

86573 

5 r 554 

80687 

53 o 4 i 

84774 

545 1 3 

83835 

55968 

82871 

58 

3 

50076 

86559 

5 1579 

85672 

53 o 66 

84769 

54537 

838 19 

55992 

82855 

5 ? 

4 

5 oioi 

86544 

5 1604 

8565 7 

53091 

84743 

5456 i 

838 o 4 

56 oi 6 

82839 

56 

5 

5 oi 26 

8653 o 

51628 

85642 

53 11 5 

84728 

54586 

83788 

66040 

82822 

55 

6 

5 oi 5 i 

865 i 5 

5 i 653 

85627 

53 140 

84712 

54610 

83 77 2 

56 o 64 

82806 

54 

7 

60176 

865 oi 

51678 

856 12 

53 164 

84697 

54635 

83756 

56 o 88 

82790 

53 

8 

50201 

86486 

51703 

85597 

53 i 8 g 

84681 

64669 

83 7 4 o 

56 112 

82773 

021 

9 

60227 

86471 

51728 

85582 

53214 

84666 

54683 

83724 

56 1 36 

82757 

5 1 

IO 

50252 

86457 

5 i 753 

8556 7 

53238 

84660 

54708 

83708 

56 160 

82741 

5 o 

11 

50277 

86442 

51778 

8555 1 

53263 

84635 

54732 

83692 

56 1 84 

82724 

49 

j 12 

5o3o2 

86427 

5 i 8 o 3 

85536 

53288 

84619 

1 64766 

83 67 6 

56208 

82708 

48 

1 13 

5 o 327 

86413 

51828 

85521 

533 12 

84604 

5478 i 

8366 o 

56232 

82692 

47 

1 14 

5 o 352 

86398 

5 1 852 

855 o 6 

53337 

84588 

64806 

83645 

56256 

82675 

46 

i 5 

5 o 377 

86384 

51877 

86491 

5336 i 

84573 

54829 

83629 

56280 

82659 

45 

16 

5 o 4 o 3 

8636 9 

51902 

85476 

53386 

84067 

54854 

836 1 3 

563 o 5 

82643 

44 

17 

50428 

86354 

5 ig 2 T 

85461 

5341 1 

84542 

54878 

83097 

56329 

82626 

43 

18 

5 o 453 

8634 o 

51952 

80446 

53435 

84026 

54902 

8358 1 

56353 

82610 

42 

19 

50478 

86325 

51977 

8543 i 

53460 

845 i i 

54927 

83565 

56377 

8209.3 

4 i 

20 

5 o 5 o 3 

863 10 

52002 

80416 

53484 

84495 

54951 

83549 

56401 

82077 

4 o 

21 

5 o 528 

86295 

52026 

85401 

53509 

84480 

54970 

83533 

06426 

8256 i 

3 9 

22 

5 o 553 

86281 

52 o 5 i 

85385 

53534 

84464 

54999 

83O17 

56449 

82644 

38 

23 

50578 

86266 

52076 

85370 

53558 

84448 

55024 

83 ooi 

56473 

82528 

37 

24 

5 o 6 o 3 

86261 

52101 

85355 

53583 

84433 

50 o 48 

83485 

56497 

825 11 

36 , 

2 5 

50628 

86237 

52126 

8534 o 

53607 

84417 

55072 

83469 

56521 

82495 

35 

i 26 

5 o 654 

86222 

52 i 5 i 

85325 

53632 

84402 

55097 

83453 

56545 

82478 

34 ! 

27 

60679 

86207 

52175 

853 io 

53656 

84386 

55 121 

83437 

5 6 569 

82462 

33 | 

j 28 

60704 

86192 

52200 

85294 

5368 i 

84370 

55 1 45 

83421 

565 9 3 

^82446 

32 ) 

29 

60729 

86178 

52225 

86279 

63700 

84355 

60169 

834 o 5 

56617 

82429 

3 i 

j 3 o 

50764 

861 63 

5225 o 

86264 

53780 

84339 

55194 

833 S 9 

06641 

82413 

3 o 

3 i 

60779 

86148 

52275 

86249 

53754 

84324 

55 qi 8 

83373 

56665 82396 

29' 

32 

5 o 8 o 4 

8 oi 33 

52299 

85234 

53779 

843 o 8 

55242 

83356 

56689 

8238o 

28 

33 

60829 

86119 

52324 

86218 

538 o 4 

84292 

55266 

83340 

56713 

82363 

27 

34 

5 o 854 

86104 

52349 

852 o 3 

53828 

84277 

55291 

83324 

56 7 36 

82347 

26 

35 

50879 

86089 

52374 

85 i 88 

53853 

84261 

553 1 5 

83 3 08 

56760 

8233o 

20 

36 

50904 

86074 

52399 

86173 

53877 

84245 

55339 

83292 

56784 

82314 

24 

37 

50929 

86069 

5242.3 

85 167 

53902 

84230 

55363 

83276 

568 o 8 

82297 

23 

38 

5 oq 54 

86045 

52448 

85 i 42 

53926 

84214 

55388 

83260 

56832 

82281 

22 

3 g 

5 oq 7 Q 

860 3 0 

52473 

85 i 27 

53961 

84198 

55412 

83244 

56856 

82264 

21 

40 

5 1004 

8601 5 

52498 

85 112 

53975 

84182 

55436 

83228 

56 S 8 o 

82248 

20 

I 4 i 

51029 

86000 

62622 

85 oq 6 

54000 

84167 

55460 

83212 

00904 

82281 

* 9 ! 

] 42 

5 io 54 

80986 

62647 

85 o 8 i 

54024 

84161 

55484 

83 i 9 5 

56928 

82214 

18! 

43 

5 1079 

86970 

52672 

85 o 66 

54049 

84 i 35 

555 o 9 

83179 

06952 

82198 

I 7 1 

44 

5 i 104 

85 g 56 

52597 

85 o 5 1 

54073 

84120 

55533 

83 1 63 

66976 

82181 


45 

51129 

86941 

52621 

85 o 35 

54097 

84104 

55557 

83147 

57000 

82 i 65 

10; 

! 46 

5 i 1 54 

85926 

52646 

85 o 2 o 

54122 

84088 

5558 i 

83 1 3 1 

57024 

82148 

*’4 

47 

5 1179 

86911 

52671 

85 oo 5 

54146 

84072 

556 o 5 

83 ii 5 

57047 

82 i 32 

i 3 , 

48 

5i2o4 

86896 

52696 

84 q 8 q 

54171 

84057 

5563 o 

83 og 8 

57071 

82 ii 5 

12 1 

49 

51229 

8588 1 

52720 

•84974 

54196 

84041 

55654 

83o82 

57095 

82098 

", 

5 o 

51254 

85866 

52745 

849O9 

54220 

84026 

55678 

83 g 66 

57119 

82082 

iaj 

5 i 

5 1279 

8585 i 

52770 

84943 

54244 

84009 

55702 

83 o 5 o 

57143 

82060 

9 

52 

5 i 3 o 4 

85836 

62794 

84928 

54269 

83994 

55726 

83 o 34 

57167 

82048 

8 

53 

5 1329 

85821 

52819 

8491 3 

54293 

83978 

5575 o 

S 3 oi 7 

57191 

82 o 3 o 

7 

54 

5 i 354 

858 o 6 

52844 

84897 

64317 

83962 

55 77 5 

83 ooi 

57215 

820 i 5 

6 

55 

5 1379, 

85792 

02869 

84882 

54342 

83946 

55799 

82985 

5 7 238 

81999 

5 

56 

5 1404| 

85777 

02893 

84866 

54366 

83930 

55823 

82969 

57262 

81982 

4 

57 

5 i 429 : 

86762 

52918 

84861 

54391 

839 i 5 

55847 

82953 

57286 

81965 

3 

58 

5 i 454 | 

86747 

52943 

84836 

54416 

83899 

55871 

82 9 36 

57810 

81949 


59 

5 i 479 I 

86732 

52967 

84820 

54440 

83883 

558 9 5 

82920 

5,7334 

819.82 

2 

M 

C. S. ! 

S. 

c. s. 

S. 

C. S. 1 

S. 

C. S. 

S. 

C. S. 

S. 

A1 

_J 

59 Deg. 

58 Deg. 

5 T Deg. 

56 Deg. 

55 Deg.^ 

- -.*4 




































































































70 


A TABLE OF NATURAL SINES. 


- 

35 Deg. 

M 

s. 0. s. 

c 

57358 81915 

1 

57381 81899 

2 

57405 81882 

3 

57429 81 865 j 

4 

57453, 81848 

5 

57477 81 83 2 

6 

575 oi 8181 5 

7 

57524' 81798 

8 

57548, 81782 

9 

57572! 81765 

10 

57696 81748 

11 

57619 81731 

12 

67643 81714 

i 3 

57667 81698 

14 

57691: 81681 

i 5 

57715 81664 

16 

57738! 81647 

*7 

57762! 8 i 63 i 

18 

57786! 81614 

*9 

57810 81597| 

20 

57833 j 8 i 58 o] 

21 

57857 j 81 563 1 

22 

67881 81 546 

23 

57904' 8 i 53 o 

24 

57928! 81 5 1 3 

25 

67952! 81496 

26 

67976] 8 i 479 

27 

67999] 81462 

28 

58023 8 i 445 

29 

58047 81428 

3 o 

58070 81412 

3 i 

58094] 8 i 3 g 5 

32 

58 118! 81378 

33 

58 i 4 i 8 i 36 i 

34 

58 i 65 81 344 

35 

58189! 81327 

36 

582121 8 i 3 io 

37 

58236 ] 81293 

38 

5826 o; 81276 

39 

582831 812J9 

4 o 

4 * 

583 o 7 ! .^42 
5833 o ! 81225 

42 

583541 81208 

43 

58378] 81191 

44 

584 oi| 81174 

45 

58425] 81167 

46 

58449! 81140! 

47 

58472; 81123| 

48 

584961 81106 

49 

680191 81089! 

5 o 

58543 ' 81072 

01 

58067] 81060 

52 

58090 8 io 38 

53 

58614] 81021 

04 

58637 81004 

55 

5866 1 80987 

56 

5 1 

58 

58684 80970 
58708; 8 og 53 

68731! 80936 

5 9 

58755 80919 

M 

c. s, | s. 


54 Deg. 


36 Beg. 


0 . S. 


58779 

588 o 2 

58826 

58849 

588 7 3 

588 9 6 

58920 

58943 

58967 

58990 

59014 

59037 

5 go 6 i 

69084 

59108 

59131 

69 1 54 

59178 

59201 

59225 

59248 

59272 

59295 

5 g 3 i 8 

59342 

5 g 365 

59389 

5 g 4 12i 

5 q 4 ^ 6 | 

59459' 

59482 

59006 

596291 

59552 

59576 

59599I 

59622! 

59646 

59/% 

59693 

59716 

59739 

59763 

59786 

59809 

59832 

59856 

59879 

59902 

59926 

5 99 4 9 

59972 

59993 

60019 

60042 
6 oo 65 
60089 
60112 
6 oi 35 
601 58 


0 . S. 


80902[ 
8 oo 85 j 
808671 

8 o 85 o 
8 o 833 
80816 
80799 
807821 
80766! 
80748 
80780 
80713 
80696 
80679 
8^602 

80644 

80627 
80610 
805981 
80576! 
8 o 558 | 
8 o 54 i! 
8 o 524 | 
80507 
804891 
80472! 
8 o 455 | 
8 o 438 ! 
80420 
804031 
8 o 386 ! 

8 o 368 

8 o 35 i 

8 o 334 

8 o 3 16 

8029 

80282 

80264 

80247 

8 o 23 o 

80212 

80195 

80178 

80160 

8 oi 43 

80125 

80108 

80091 

80073 

8 oo 56 

8 oo 38 

80021 

8 ooo 3 

79986 

79968 

7 99 5 1 

79934 

79916 

79899 

79881 

s 7 ~ 


* 4 ^ 


37 Deg. 


C. S. 


60182! 

6 o 2 o 5 

60228; 

6 o 25 iI 

60274 

602981 

6 o 32 iI 

6 o 344 

60367 

60390 

60414 

60437 

60460 

60483 

6 o 5 o 6 

60029 


79864 
79846 
79829 
79811 

79793 

79776 

79758 

79741 

79723 

79706 

79688 

79671 

79653 

79635 

79618] 

79600 


6 o 553 ! 7 9 583 
60576] 79665 
6 o 5 99 j 79347 
606221 7953o 
60643' 79512 
60668 79494 


53 Deg. 


60691 
60714 
60738 
60761 
60784 
60807 
6 o 83 o 
6 o 853 
60876 

60899 

60922 

60945 

60968 

.!° 99 * 

6ioi5 

6 io 38 

61061 

61084 

61107 
61 i 3 o 
611 53 
61176 
61199 
61222 

61245 
61268 
61291 
61 3 14 
61337 
6 i 36 o 
61 383 
61406 
61429 
61461 
61474 
61497! 

61620 

6i543 


C. S. 


79477 

79459 

79441 

79424 

79406 

79388 

7937 1 
79353 
79335 ] 

79 3i8 | 
793 oo| 
79282 j 
79264! 

79247 : 

79229. 

. 792 " 

79193 

79! 58 
79U0 
79122 
79105 
79087 
79069 

79 o 5 i 

79 o 33 

79015 

78908 

78980 

78962 

78944 

78926 

78908 

78891 

78873 

78855 

78837 

78819 


S. 


52 Deg. 


38 Deg. 


S. 

6 1 566 
61689 
61612 
6 i 635 
6 1 658 
61681 

61704 

61726 

61749 

61772 

61795 

61818 

61841 

61864 

61887 

61909 

61932 

61955 

61978 

62001 

62024 
62046; 
62069 
62092] 
6211 5 
621 38 
62160 

62183 

62206 
62229 
6225 1i 

62274; 
62297] 
62320! 
62342 1 
62365 
62388 ] 
62411 

62433 

62466] 

62479' 

62502 

62624 

62547 

62570 

62592] 

62615! 

62638 ] 

62660] 

62683 ] 

62706 

62728, 

62751] 

627741 

62796 

62819 

62842 

62864 

62887 

62909 

c 7 s 7 


39 Deg. 


C. S._ 

78801 

78783 

78765 

78747 

78729 

78711 

78694 

78676 

786581 

78640 1 

78622; 

78604! 

78586 ] 

78568 ' 

7855 o] 

78532 ] 

785 i 4 ] 

78496] 

78478 

78460 

78442 

78424; 

78400 j 

78387 

78369] 

78301 

78333 

7831 5 

78297 

78279 

78261 

78243 

78225 

78206 

78188 

78170 

78162 

781341 

78116! 

78098! 

78079] 

78061 

78043 j 

78025' 

78007 

77988 

77970 

779 52 

779 3 4 

779 l6 

77897 

77879 

77861 

77843 

77824 

77806] 

77788; 

77769 

77 7 5 i 

77733 


777 >o 
77696 
77678 
77660 
77641 
77623 
77605 
77586 
77 568 i 
7755o| 5i 
7753i i 5 o 


773*3 

77494 

77476 


S. 


51 Deg. 


s. c. s. 

62982 
62955 
62977 
63 ooo 
63022 
63 o 45 
63 068 
63090 
63 11 31 
63 1 35 j 
63 1 58 
63 i 8 o' 

63 2 o 3 [ 

63225 ; 

63 248 ; 

632711 

63293 1 
633 16! 

63338 
6336 i 
63383 
63406! 

63428 
63401 
63473 
63496 
63 5 18 
63540 
63563 
63585 
636 oS 


M 

60 

5 9 

58 1 

57 i 

56 

55 ! 

54 

53 

52 


49 

48 

47 


77458 46 
77439 45 
77421 44 

77402 43 

77384 1 42 

77366 ; 41 
77347 ] 4 o 
77329 1 3 
773 io] 3 
77292] 37 
77273 36 
rr 35 
34 
33 
32 
3 i 
3 o 


77255 

77236 

77218 

77*99 

77181 

77162 


63 o 3 o 

63653 

63675 

636 9 8 

63720 

637421 

63765! 

63787! 

638 io] 

63832 ] 

638541 

63877! 

63899] 

63922 

63 g 44 

63 966 
63989 
64011 
64033 
640 56 
64078 
64100] 

64123 

64145 

64167 

64190 

64212 

64234 

64266 

C 7 s 7 


77*44 
77126 
77*07 27 
77088 
77070 
77 o 5 i 
77 o 33 
77014! 22 

76996 21 
76977 
76959 


29 

28 


26 

25 

24 

23 


20 

*9 


16 

i 5 

14 

i 3 

12 


76940 18 
76921 17 

76903 
76884 

76866 

76847 

76828 
76810] n 
76791] 10 
76772! 9 

76704! 8 
76735 
76717 
76698 
766791 
76661 
76642 
76623 


50 Deg. 


M 







































































































A TABLE OF NATURAL SINES. 


n 



40 Deg. 

41 Deg. 

42 Deg. 

43 

Deg. 

44 Deg. 


M 

S. 

a s. 

S. 

C. S. 

S. 

a S. 

S. 

C. S. 

S. 

| C. S. 

M 

0 

64279 

76604 

60606 

7 5 47 i 

66913 

74314 

68200 

73135 

69466 

71934 


i 

643 oi 

76586 

66628 

76462 

66935 

74295 

68221 

73 ii 6 

69487 

71914 

5o 

2 

64323 

76567 

6565o 

75433 

66956 

74276 

68242 

73096 

69008 

71894 

58 

3 

64346 

76548 

65672 

75414 

66978 

74266 

68264 

73076 

69629 

71873 

57 

4 

6436d 

76530 

65694 

75396 

66qqq 

74237 

68285 

73o56 

69649 

7i853 

56 

5 

64390 

765 I 

65716 

j 75375 

67021 

74217 

683o6 

73o36 

69670 

7i833 

55 

6 

64412 

i 76492 

1 65 7 38 

75356 

67043 

74198 

68327 

73 oi 6 

6q5qi 

71813 

54 

7 

64435 

76473 

| 66769 

75337 

67064 

74178 

68349 

72996 

6961 2 

71792 

53 

8 

64467 

76455 

65781 

753 i 8 

67086 

74i59 

68370 

72976 

69633 

71772 

52 

9 

64479 

76436 

65So3 

75299 

67107 

74 i 39 

68391 

72957 

69604 

71762 

5i 

IO 

64601 

76417 

65825 

76280 

67129 

74120 

68412 

72937 

69670 

71732 

5o 

11 

64624 

76398 

65847 

75261 

67151 

74100 

68433 

72917 

69696 

71711 

49 

12 

64^46 

76380 

66869 

75241 

67172 

74080 

68455 

72897 

69717 

71691 

40! 

i3 

64668 

76361 

66891 

|s 75222 

67194 

74061 

68476 

72877 

69737 

71671 

1 471 

U 

64690 

1 76342 

65913 

76203 

67216 

74041 

68497 

72867 

69708 

71660 

46 

i5 

64612 

76323 

65935 

76184 

67237 

74022 

685x8 

72837 

69779 

7io3o 

45 

16 

64635 

76304 

65q56 

76165 

67258 

74002 

6853 9 

72817 

69800 

71610 

44 

li 

64667 

76286 

66978 

76146 

67280 

73983 

68561 

72797 

69821 

71590 

43 

i8 

64679 

76267 

66000 

76126 

67301 

73963 

68582 

72777 

69842 

71069 

42 


64701 

76248 

66022 

75107 

67823 

73944 

686o3 

72757 

69862 

71549 

41 

20 

64723 

76229 

66o44 

i 75088 

67344 

73924 

68624 

72737 

69883 

71629 

40 

21 

64746 

76210 

66066 

75069 

67366 

73904 

68640 

72717 

69904 

715o8 

39 

22 

64768 

76192 

66088 

75 o 5 o 

67387 

73885 

68666 

72697 

69925 

71488 

38 

23 

64790 

76173 

66109 

75 o 3 o 

67409 

73865 

68688 

72677 

69946 

71468 

37 

24 

64812 

76154 

66131 

75 oii 

67430 

73846 

68709 

72667 

69966 

71447 

36 

25 

64834 

76135 

66153 

74992 

67462 

73826 

68730 

72637 

69987 

71427 

35! 

26 

64856 

76116 

66176 

74973 

67473 

73806 

68751 

72617 

70008 

71407 

34 

21 

64878 

76097 

66197 

74953 

67495 

73787 

68772 

72597 

70029 

71386 

33! 

28 

64901 

76078 

66218 

74934 

67516 

73767 

68793 

72577 

70049 

71366 

32! 

n 9 

64923 

76069 

! 66240 

74916 

67538 

73747 

68814 

72007 

70070 

7i345 

3i 1 

3o 

64945 

76041. 

j 66262 

74896 

67559 

73728 

68835 

72537 

70091 

71825 

3o 1 

3i 

64967 

76022 

66284 

74876 

67580 

73708 

6885 7 

72617 

70112 

7i3o5 

29 

32 

64989 

76003 

663o6 

74807 

67602 

73688 

68878 

72497 

70i32 

71284 

28 

33 

65oi 1 

70984! 

66327 

74838 

67623 

73669 

68899 

72477 

70i53 

71264 

27 

34 

65o33 

75965 

66349 

74818 

67645 

73649! 

68920 

72457 

70174 

71243 

26 

35 

65o55 

70946! 

6637! 

74799 

67666 

73629; 

68941 

72437 

70195 

71223 

20 

36 

65077 

70927! 

66393 

74780 

67688 

73610 

68062 

72417 

70215 

71203 

24 

37 

66099 

75508 

66414 

74760 

67709 

73690 

68988 

72397 

70286 

71182 

23 

38 

65l22| 

758891 

66436 

74741 

67730 

73570, 

69004 

72377 

70267 

71162 

22 

3 9 

66144 

75870 

66468 

74722 

67762 

73551 i 

69026 

72307 

70277 

71141 

21 

40 

65166 

75851 

66480 

74703 

67773 

7353 i 

69046 

72337 

70298 

71121 

20 

4i 

65188 

7 58321 

665oi 

74683 

67795 

735 :i 

69067 

72317 

70319 

71100 

19 

42 

652io 

70813 

66523 

74664 

67816 

78491 

69088 

72297 

70339 

71080 

18 

43 

65232 

75794 

66549 

74644 

67637 

73472 

69109 

72277 

70360 

71069 

17 

44 

65254 

75 77 5! 

66566 

74626 

67809 

73462 

69130 

72267 

70381 

71089 

16 

45 

60276 

76766! 

66588 

74606 

67880 

73432 

69151 

72236 

70401 

71019 

151 

46 

65298 

7 573 s! 

66610 

74686 

67901 

73412 

69172 

72216 

70422 

7°99^ 

14 

47 

65320 

76719 

6663 2 

74667 

67923 

733 9 3 

69198 

72196 

70443 

70978 

1 3 

48 

65342 

76699 

66603 

74948 

67944 

73373: 

69214 

72176 

70463 

70907 

12 j 

49 

65364 

7 568 oi 

66675 

74628 

67965 

7 3353l 

69280 

72166 

70484 

70937 

11! 

5o 

65386 

76661 1 

66697 

74009 

67987| 

73333| 

69266 

72136 

7 o 5 o 5 

70916 

10 

5i 

66408 

70642 

66718 

74489 

68008 

73314| 

69277 

72116 

7 o 525 i 

70896 

9 

52 

6543o 

70623 1 

66740 

74470 

68029; 

73294 

692981 

72095 

706461 

70876 

8 

53 

66462 

70604; 

66762 

7445 i 

68o5i 

73274 

69319 

72075 

70067 

7o855 

7 

54 

65474 

7 5585| 

66783 

74431 

68072 

73254! 

69340 

72o55 

70687 

70834 

6 

55 

66496 

7 5566j 

668o5 

74412 

68093 

73234 

69361 

72o35 

70608 

70813 

5 

56 

65518 

76647! 

66827 

74392 

68115 

73210 

69382 

72016 

70628 

70793 

4 

5 7 

6554o 

75628! 

66848 

74373 

68i36 

73195 

69403 

71995 

70649 

70772 

3 

; 58 

65562 

7OO09 

66870 

74353 

68167 

73170 

69424 

71974 

70670 

70702 

2 

1 &9 

65584 

76490 

66891 

74334 

68179 

73155, 

69445 

71964 

70690 

70731 

1 

60 | 

656o6 

76471 

66913 

743 i 4 

68200 

73135j 

69466 

71934 

70711 

70711 

01 

~M | 

c.s. 1 

S. 

C. S. 

S. 

C. S. 

S. 

a s. 

S. 

a s. 

S. 

m| 

1 

49 Deg. 

AS Deg. 

47 Deg. 

46 Deg. 

45 Deg. 

i 


























































































































TRAVERSE TAHLE. 


2 


Distance. 

i Deg. 

5 Deg. 

2 Deg. 

Distance.! 

L&ti 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

* 1 

1.00 

0.00 

1.00 

0.01 

1.00 

0.01 

1 

2 

2.00 

0.01 

2.00 

0.02 

2.00 

0.03 

O 

M 

3 

3.00 

0.01 

3.00 

0.03 

3.00 

0.04 

3 

4 

4.00 

0.02 

4.00 

0.03 

4.00 

0.05 

4 

5 

5.00 

0.02 

5.00 

0.04 

5.00 

0,07 

5 

6 

6.00 

0.03 

6.00 

0.05 

6.00 

O.OS 

6 

7 

7.00 

0.03 

7.00 

0.06 

7.00 

0,09 

7 

8 

8.00 

0.03 

8.00 

0.07 

8.00 

0.10 

8 

9 

9.00 

0.04 

9.00 

0.08 

9.00 

0.12 

9 

10 

10.00 

0.04 

10.00 

0.09 

10.00 

0.13 

10 

11 

11.00 

0.05 

11.00 

0.10 

11.00 

0.14 

11 

12 

12.00 

0.05 

12.00 

0.10 

12.00 

0.16 

12 

13 

13.00 

0.06 

13.00 

0.11 

13.00 

0.17 

13 

14 

14.00 

0.06 

14.00 

0.12 

14.00 

0.18 

14 

15 

15.00 

0.07 

15.00 

0.13 

15.00 

0.20 

15 

16 

16.00 

0.07 

16.00 

0.14 

16.00 

0.21 

16 

17 

17.00 

0.07 

17.00 

0.15 

17.00 

0.22 

17 

18 

18.00 

0 08 

18 00 

0.16 

18.00 

0.24 

18 

19 

19.00 

0.08 

19.00 

0.17 

19.00 

0.25 

19 

20 

20.00 

0.09 

20.00 

0.17 

20.00 

0.26 

20 

21 

2 ! .00 

0.09 

21.00 

0.18 

21.00 

0.27 

21 

22 

22.00 

0.10 

22.00 

0.19 

22.00 

0.29 

22 

23 I 

23.00 

0.10 

23.00 

0.20 

23.00 

0.30 

23 

24 

24.00 

0.10 

24.00 

0.21 

24.00 

0.31 

24 

25 

25.00 

0.11 

25.00 

0.22 

25.00 

0.33 

25 

26 1 

26.00 

0.11 

26.00 

0.23 

26.00 

0.34 

26 

27 | 

27.00 

0.12 

27.00 

0.24 

27.00 

0.35 

27 

28 | 

28.00 

0.12 

28.00 

0.24 

28.00 

0.37 

28 

29 1 

29.00 

0.13 

29.00 

0.25 

29.00 

0.38 

29 

30 

30.00 

0.13 

30.00 

0.26 

30.00 

0.39 

30 

31 

31.00 

0.14 

31.00 

0.27 

31.00 

0.41 

31 

32 

32.00 

0.14 

32.00 

0.28 

32.00 

0.42 

32 

33 

33.00 

0.14 

33.00 

0.29 

33.00 

0.43 

33 

34 

34.00 

0.15 

34.00 

0.30 

34.00 

0.45 

34 

35 

35.00 

0.15 

35.00 

0.31 

35.00 

0.46 

35 

36 

36.00 

0.16 

36.00 

0.31 

36.00 

0.47 

36 

37 

37.00 

0.16 

37.00 

0.32 

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89| Deg. 

89* 

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89£ Deg. 

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TKAVEKSE TAHLE. 


3 


Distance. 

1 

4 Deg. 

k Deg. 

2 Deg. 

~1 

O 

t— • 

GQ 

3 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

51.00 

0.22 

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51.00 

0.67 

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52 

52.00 

0.23 

52.00 

0.45 

52.00 

0.68 

52 

53 

53.00 

0.23 

53.00 

0.46 

53.00 

0.69 

53 

54 

54.00 

0.24 

54.00 

0.47 

54.00 

0.71 

54 

55 

55.00 

0.24 

55.00 

0.48 

55.00 

0.72 

55 

56 

50.00 

0.24 

56.00 

0.49 

56.00 

0.73 

56 

57 

57.00 

0.25 

57.00 

0.50 

57.00 

0.75 

57 

58 

58.00 

0.25 

58.00 

0.51 

57.99 

0.76 

58 

59 

59.00 

0.26 

59.00 

0.51 

58.99 

0.77 

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60 

60.00 

0.26 

60.00 

0.52 

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0.79 

60 

61 

61.00 

0.27 

61.00 

0.53 

60.99 

0.80 

61 

62 

62.00 

0.27 

62.00 

0.54 

61.99 

0.81 

62 

63 

63.00 

0.27 

63.00 

0.55 

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0.82 

63 

64 

64.00 

0.28 

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65 

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66 

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4 


TRAVERSE TAHLK. 


5 1 

3 

r* 

i 

1 Deg. 

U Deg. 

U Deg. 

If Deg. ! 

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W 

W* 

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P 

3 

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Dep. 

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Dep. 

3 1 

O 

o 

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2 

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1.00 

0.02 

1.00 i 

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1.00 

0.03 

1 

2.00 

0.03 

2.00 

0.04 

2.00 

0.05 

2.00 

0.06 

2 

3 

3.00 

0.05 

3.00 

0.07 

3.00 

0.08 

3.00 

0 .09 

3 

4 

4.00 

0.07 

4.00 

0.09 

4.00 

0.10 

4.00 

0.12 

4 

5 

5.00 

0.09 

5.00 

0.11 

5.00 

0.13 

5.00 

0.15 

5 

6 

6.00 

0.10 

6.00 

0.13 j 

6.00 

3; 16 

6.00 

0.18 

6 

7 

7.00 

0.12 

7.00 

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7.00 

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7.00 

0.21 

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8 

8.00 

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0.63 

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0.86 

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29 

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0.76 

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30 

30.00 

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31 

31.00 

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32 

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TRAVERSE TABLE. 


5 


y 

a? 

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P 

1 Deg. 

I 

H Deg. 

H Dc s- 

l| Deg. 

5 

r £ 

3 

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55 

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60 

61 

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62 

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1.62 

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1.89 

62 

63 

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1.10 

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1.37 

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1.65 

62.97 

1.92 

63 

64 

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1.12 

63.98 

1.40 

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1.68 

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64 

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1.42 

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1.70 

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^5 

66 

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1.44 

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1.73 

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2.02 

66 

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1.75 

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2.05 

67 

68 

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1.48 

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1.78 

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2.08 

68 

69 

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1.51 

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1.81 

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2.11 

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70 

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1.22 

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1.53 

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1.83 

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2.14 

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73.97 

2.26 

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1.64 

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J .96 j 

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2.29 

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1.33 

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2.32 

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1.34 

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1.68 

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2:02 

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2.35 

77 

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1.36 

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1.70 

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2.04 

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2.38 

78 

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1.38 

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1.72 

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2.07 

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2.41 

79 

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2.09 

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2.44 

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2.50 

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2.30 

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2.81 

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2.43 

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d 

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s 

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88? Deg. 

88 i 

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i. - 













































































































6 


TKAVEKSH TAHLE. 


5 

tr+ 

P® 

tj 

o 

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2 Deg. 

24 Deg. 

~2 De S- 

2| Deg. 

O 

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Lat. 

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Dep. 

Lat. 

Dep 

Lat. 

- 

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>«■ 

o 

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0.07 

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0.08 

2.00 

0.09 

2.00 

0.10 

2 

3 

3.00 

0.10 

3.00 

0.12 

3.00 ! 

0.13 

3.00 

0.14 

Q 

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4 

4.00 

0.14 

4.00 

0.16 

4.00 1 

0.17 

4.00 

0.19 

4 

5 

5.00 

ft. 17 

5.00 

0.20 

5.00 

0.22 

4.99 

0.24 

5 

6 

6.00 

0.21 

6.00 

0.24 

5.99 

0.26 

5.99 

0.29 

6 

7 

7.00 

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0.27 

6.99 

0.31 

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0.34 

7 

8 

7.99 

0.28 

7.99 1 

0.31 

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0.35 

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0.38 

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9 

8.99 

0.31 

8.99 

0.35 

8.99 

0.39 

8.99 

0.43 

9 

10 

9.99 

0.35 

9.99 

0.39 

9.99 

0.44 

9.99 

0.48 

10 

11 

10.99 

0.38 

10.99 

0.43 

10.99 

0.48 

10.99 

0.53 

11 

12 

11.99 

0 42 i 
0.45 I 

11.99i 

0.47 

11.99 

0.52 

11.99 

0.58 

12 

13 

12.99 

12.99 ! 

0.51 

12.99 

0.57 

12.99 

0.62 

13 

14 

13.99 

0.49 

13.99 

0.55 

13.99 

0.61 

13.98 

0.67 

14 

15 

14.99 

0.52 

14.99 

0.59 

14.99 

0.65 

14.98 

0.72 

15 

16 

15.99 

0.56 

15.99 

0.63 

15.99 

0.70 

15.98 

0.77 

16 

17 

16.99 

0.59 

16.99 

0.67 

16.98 

0.74 

16.98 

0.82 

17 

18 

17.99 

0 . 63 

17.99 

0.71 

17.98 

0.79 

17.98 

0.86 

18 

19 

18.99 

0.66 

18.99 

0.75 

18.98 

0.83 

18.98 

0.91 

19 

20 

19.99 

0.70 

19.98 

0.79 

19.98 

0.87 j 

19.98 

0 . 96 

20 

21 

20.99 

0.73 

20.98 

0.82 

20.98 

0.92 

20.98 

1.01 

21 

22 

21.99 

0.77 

21.98 

0.86 

21.98 

0.96 

21.97 

1.06 

22 

23 

22.99 

O.bO 

| 22.98 

0.90 

22.98 

1.00 

22.97 

1.10 

23 

24 

23.99 

0.84 ! 

23.98 

0.94 

23.98 

1.05 

| 23.97 

1.15 

24 

25 

24.98 

0.87 

124.99 

0.98 

24.98 

1.09 

;24.97 

1.20 

25 

26 

25.98 

0.91 

25.98 

1.02 

25.98 

1.13 

25.97 

1.25 

26 

27 

26. B8 

0.94 

26.98 

1.06 

26.97 

1.18 

26.97 

1.30 

27 

28 

27.98 

0.98 

27.98 

1.10 

27.97 

1.22 

27.97 

1.34 

28 

29 

28.98 

1.01 

28.98 

1.14 

28.97 

1.26 

23.97 

1.39 

29 

30 

29.98 

1.05 

29.98 

1.18 

29.97 

1.31 

29.97 

1.44 

30 

31 

30.98 

1.08 

30.98 

1.22 

30.97 

1.35 

30.96 

1.49 

31 

32 

31.98 

1 .12 

31.98 

1.26 

31.97 

1.40 

j31.96 

1 .54 

32 

33 

32.98 

1.15 

32.97 

1.30 

32.97 

1.44 

32.96 

1.58 

33 

34 

33.98 

1.19 

33.97 

1.33 

33.97 

1.48 

33.96 

1.63 

34 

35 

34.98 

1 .22 

34.97 

1.37 

34.97 

1.53 

34.96 

1.68 

35 

36 

35.98 

1.26 

35.97 

1.41 

35.97 

1.57 

i35.96 

1.73 

36 

37 

30.98 

1 .29 

36.97 

1.45 

36.96 

1.61 

!36.96 

1.78 

37 

38 

37 • 98 

1.33 

37.97 

1.49 

37.96 

1.66 

I 37.96 

1.82 

38 

39 

38.98 

1.36 

38.97 

1.53 

38.96 

1 .70 

138.96 

1.87 

39 

40 

39.98 

1.40 

39.97 

1 57 

39.96 

1.75 

39.95 

1.92 

40 

41 

40.98 

1.43 

40.97 

1.61 

40.96 

1.77 

40.95 

1.97 

41 

42 

41.97 

1.47 

41.97 

1.65 

41.96 

1 .S3 

41.95 

2.02 

42 

43 

42.97 

1.50 

42.97 

1.69 

42.96 

1.88 

42.95 

2.06 

43 

44 

43.97 

1.54 

43.97 

1.73 

43.96 

1.92 

43.95 

2.11 

44 

45 

44.97 

1.57 

44.97 

1.77 

44.96 

1.96 

44.95 

2.16 

45 

46 

45.97 

1 1.61 

45.96 

1.81 

45.96 

2.01 

45.95 

2.21 

46 

47 

46.97 

1.64 

46.96 

1.85 

40.96 

2.05 

46.95 

2.25 

47 

48 

47.97 

1.68 

47.96 

1.88 

47.95 

2.09 

47.95 

2.30 

48 

49 

48.97 

1.71 

48.96 

1.92 

48.95 

2.14 

48.94 

2.35 

49 

50 

49.97 

1.74 

49.96 

1.96 

49.95 

2.18 

49.94 

2.40 

50 

O 

o 

£ 

' Dep 

"Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 Lat. 

1 

03 

V 

c 

:d 

73 

• rH 

G 

88 Deg. 

87^ Deg. 

1 

87± 

Deg. 

87} Deg. 

cd 

73 

! * 
i w-* 

i 



















































































































TRAVERSE TABLE. 


7 


zn 

r* 

P 

2 Deg. 

i 

2* Deg. 

2- 

Deg. 

n Deg. 

j o 

& 

P 

3 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

s 

o 

CD 

5l 

50.97 

1.78 

50.96 

2.00 

50.95 

2.22 

50.94 

2.45 

51 

52 

I 51.97 

1.81 

51.96 

2.04 

51.95 

2.27 

51.94 

2.50 

52 

52 

52.97 

1.85 

52.96 

2.08 

52.95 

2.31 

52.94 

2.54 

53 

54 

53.97 

1.88 

53.96 

2.12 

53.95 

2.38 

53.94 

2.59 

j u 

55 

54.97 

1.92 

54.96 

2.16 

54.95 

2.40 

54.94 

2.64 

i 55 

56 

55.97 

1.95 

1 55.96 

2.20 

55.95 

2.44 

!55.94 

2 69 

56 

57 

56.97 

1.99 

i56.98 

2.24 

56.95 

2.49 

56.93 

2.73 

57 

5S 

• 57.96 

2.02 

i57.96 

2.28 

57.94 

2.53 

57.93 

2.78 

58 

59 

58.96 

2.06 

58.95 

2.32 

58.94 

2.57 

58.93 

2.83 

j 59 

69 

59.96 

2.09 

59.95 

2.36 

59.94 

o no 

59.93 

2.83 

60 

61 

60.96 

2. 13 

60,95 

2.39 

60.94 

2.66 

60.93 

2.93 

61 

62 

;61.96 

| 2.16 

61.95 

2.43 

61.94 

2.70 

,61.93 

2.97 

62 

63 

62.98 

2.20 

62.95 

2.47 

62.94 

2.75 

I 62.93 

3.02 

63 

64 

63.96 

O 0‘> 

A* . 

63.95 

2.51 

63.94 

2.79 

63.93 

3.07 

64 

65 

64.96 

2.27 

64.95 

2.55 

64.94 

2.84 

64.93 

3. 12 

65 

66 

65.96 

2.30 

65.95 

2.59 

:65.94 

2.88 

65.92 

3.17 

66 

67 66.98 

2.34 

66.95 

2.63 

86.94 

2.92 

66.92 

3.21 

67 

68 

87.96 

2.37 

67.95 

2.67 

67.94 

2.97 

67.92 

3.26 

68 

69 

88.96 

2.41 

68.95 

2.71 

68.93 

3.01 

68,92 

3.31 

69 

70 

69.96 

2.44 

69.95 

2.75 

69.93 

3.05 

89.92 

3.36 

70 

71 

70.96 

2.48 

70.95 

2.79 

70.93 

3.10 

70.92 

3.41 

71 

72 

71.96 

2.51 

71.94 

2.83 

71.93 

3. 14 

71.92 

3.45 

72 

73 

72.96 

2.55 

72.94 

2.87 

72.93 

3.18 

72.92 

3.50 

73 

74 

73.95 

2.58 

73.94 

2.91 

73.93 

3.23 

73.91 

3.55 

74 

7f> 

74.95 

2.62 

74.94 

2.94 1 

74.93 

3.27 

74.91 

3.60 

75 

78 

75.95 

2.65 

75.94 

2.98 

75.93 

3.31 

75.91 

3.65 

76 

77 

76.95 

2.69 

76.94 

3.02 ! 

76.93 

3.36 

76.91 

3.70 

77 

78 

77.95 

2.72 

77.94 

3.06 1 

77.93 

3.40 

77.91 

3.74 

78 

79 

78.95 

2.76 

78.94 

3.10 

78.92 

3.45 

78.91 

3.79 

79 

80 

79.95 

2.79 

79.94 

3.14 

79.92 

3.49 

79.91 

3.84 

80 

81 

80.95 

2.83 

80.94 

3.18 

80.92 

3.53! 

80.91 

3.89 

81 

82 

81.95 

2.86 

81.94 

3.22 

81.92 

3.58 

81.91 

3.93 

82 

83 

82.95 

2.90 

82.94 

3.26 

82.92 

3.62 

82.90 

3.98 

83 

84 

85 

83.95 

2.93 

83.94 

3.30 

83.92 

3.66 ! 

83.90 

4.03 

84 

84.95 

2.97 

84.93 

3.34 

84.92 

3.71 

84.90 

4.08 

85 

86 

85.95 

3.00 

85.93 

3.38 

85.92 

3.75 

8s O'* 

4.13 

86 

87 

86.95 

3.04 

86.93 

3.42 

86.92- 

3.79 

86.90 

4.17 

87 

88 

87.95 

3.07 

87.93 

3.45 

87.92 

3.84 

87.90 

4.22 

88 

89 

88.95 

3.11 

88.93 

3.49 

88.92 

3.88 

88.90 

4.27 

89 

90 

89.95 

3.14 

89.93 

3.53 

89.91 

3.93 

89.90 

4.32 

90 

91 

90.95 

3.18 | 

90.93 

3.57 

90.91 

3.97 

90.90 

4.37 

91 

92 

91.94 

3.21 

91.93 

3.61 

91.91 

4.01 

91.89 

4.41 

92 

93 

92.94 

3.25 1 

92.93 

3.65 

92.91 

4.06 

92.89 

4.46 

93 

94 

93.94 

3.23 I 

93.93 

3.69 

93.91 

4.10 

93.89 

4.51 

94 

S5 

94.94 

3.32 

94.93 

3.73 

94.91 

4.14 

94.89 

4.56 

95 

96 

95.9 1 

3.35 

95.93 

3.77 

95.91 

4.19 

95.89 

4.61 

96 

97 

96.94 

3.39 

96.93 

3.81 

96.91 

4.23 

98.89 

4.65 

97 

99 

97.94 

3.42 f 

97.92 

3.85 

97.91 

4.27 

97.89 

4.70 

98 

99 1 

98.94 

3.46 

98.92 

3.89 

98.91 

4.32 

98.89 

4.75 

99 

100 

99.94 

3.49 

99.92 

3.93 

99.91 

4.36 

99.8S 

4.SO 

:oo 

d 

u 

a 

Dep. 

Lac. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance. 

« Dista 
3 

1 

83 Deg. 

87J Deg. 

87^ Deg. 

87} Deg. 





















































































































8 


TKAVEKSK TABLE. 


c 

ST 

r** 

P 

3 Deg. 

3-i Deg. 

i 

Deg. 

3f Deg. 

O 
►— • 

71 

r* 

P 

3 

O 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

p 

' 1 

1.00 

0.05 

j 1.00 

0.08 

1.00 

0 .06 

l.ooi 

0.06 

1 

2 

2.00 

0. 10 

2.00 

0.11 

2.00 

0.12 

2.00 

0 13 

2 

3 

3.00 

0.10 

3.00 

0.17 

2.99 

0.18 

2.99 

9.20 

3 

4 

3.99 

0.21 

3.99 

0.23 

3.99 

0.24 

i 3.99 

0.26 

1 

5 

4.99 

0.26 

4.99 

0.2S 

4.99 

0.31 

4.99 

0.33 

i 

6 

5.99 

0.31 

5.99 

0.34 

5.99 

0.37 

5.99 

0.39 

6 

7 

6.99 

0.37 ! 

6.99 

0.40 

6.99 

0.43 

6.99 

0.46 

7 

8 

7.99 

0.42 

7.99 

0.45 

7.99 

0.49 

7.98 

0.52 

S 

9 

8.99 

0.47 

8.99 

0.51 

8.98 

0.55 

8.98 

0.59 

9 

10 

9.99 

0.52 j 

9.98 

0.57 

9.98 

0.61 

9.98 

0.65 

10 

11 

10.98 

0.58 j 

10.98 

0.62 

10.98 

0.67 

10.98 

0.72 

11 

12 

11.98 

0.63 

11.98 

0.68 

11.98 

0.73 

11.97 

0.78 

12 

13 

i2.98 

0.68 

12.98 

0.73 

12.98 

0.79 

12.97 

0.85 

13 

14 

13.98 

0.73 

13.98 

0.79 

13.97 

0.85 

13.97 

0.92 

14 

L5 

14.98 

0.79 

14.9S 

0.S5 

14.97 

0.92 

14.97 

0.98 

15 

16 

15.99 

0.84 j 

15.97 

0.91 

15.97 

0.98 

15.97 

1.05 

16 

17 

16.98 

0.89 i 

16.97 

0.96 

16.97 

1.04 

16.96 

1. 11 

17 

18 

17.93 

0.94 | 

17.97 

1.02 

17.97 

1.10 

17.96 

1.18 

18 

19 

19.93 

0.99 ! 

18.97 

1.08 

18.96 

1.16 

18.96 

1.24 

19 

20 

19.97 

1.05 j 

19.97 

1.13 

19.96 

1.22 

19.96 

1.31 

20 

21 

20.97 

1.10 

20.97 

1.19 

20.96 

1.28 

20.96 

1.37 

21 

22 

21.97 

i.i5; 

21.96 

1.25 

21.96 

1.34 

21.95 

1.44 

22 

23 

22.97 

1.20 I 

22.96 

1.30 

22.96 

1.40 

22.95 

1.50 

23 

24 

23.97 

1.26 ' 

23.96 

1.36 

23.96 

1.47 

23.95 

1.57 

24 

25 

24.97 

1.31 

24.96 

1.42 

i24.95 

1.53 

24.95 

1.64 

25 

26 

25.96 

1.36 

25.96 

1.47 

25.95 

1.59 

25.94 

1.70 

26 

27 

26.96 

1.41 

26.96 

1.53 

26.95 

1.65 

26.94 

1.77 

27 

28 

27.96 

1.47 

27.95 

1.59 

27.95 

1.71 

27.94 

1.83 

28 

29 

28.96 

1.52 

28.95 

1.64 

28.95 

1.77 

28.94 

1.90 

29 

30 

29.96 

1.57 

29.95 

1.70 | 

29.94 

1.83 

29.94 

1.96 

30 

31 

30.96 

1.62 

30.95 

1.76 

30.91 

1.S9 : 

30.03 

2.03 

31 

32 

31.96 

1.67 

31.95 

1.81 

31.94 

1.95 

31.93 

2.09 

32 

33 

32.95 

1.73 

32.95 

1.87 i 

32.94 

2.01 i 

32.93 

2.16 

33 

34 

33.95 

1.78 

33.95 

1.93 

33.94 

2.08 ! 

33.93 

2.22 

34 

35 

34.95 

1.83 

34.94 

1.98 

34.93 

2.14 

34.92 

2.29 

35 

36 

35.95 

1.88 

35.94 

2.04 

35.93 

2.20 

35.92 

2.35 

36 

37 

36.95 

1.94 

36.94 

2.10 

38.93 

2.26 

36.92 

2.42 

37 

38 

37.95 

1.99 

37.94 

2.15 

37.93 

2.32 

37.92 

2.49 

38 

39 

38.95 

2.04 

38.94 

2.21 | 

38.93 

2.38 

38.92 

2.55 

39 

40 

39.95 

2.09 

39.94 

2.27 | 

39.93 

2.44 

39.91 

2.62 

40 

41 1 40.94 

2.15 

40.93 

2.32 

40.92 

2.50 

40.91 

2.68 

41 

42 

41.94 

2.20 

41.93 

2.38i 

41.92 

2.56 

|41.91 

2.75 

42 

43 

42.94 

2.25 

42.93 

2.44 

42.92 

2.63 

142.91 

2.81 

43 

44 

43.94 

2.30 

43.93 

2.49 

43.92 

2.69 

143.91 

2.88 

44 

45 

44.94 

2.36 

44.93 

2.55 

44.92 

2.75 

1 44.90 

2.94 

45 

46 

45.94 

2.41 

45.93 

2.61 j 

45.9 i 

2.81 

; 45.90 

3.01 

16 

47 

40.94 

2.46 

46.92 

2.66 

46.91 

2.87 

|46.00 

3.07 

47 

48 

47.93 

2.51 

47.92 

2.72 

147.91 

2.93 

j 47.90 

3.14 

48 

49 

48.93 

2.56 

48.92 

2.78 

48.91 

2.99 

48.90 

3.20 

4!) 

50 

49.93 

2.62 

49.92 

2.83 

49.91 

3.05 

49.89 

3.27 

50 

6 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

ZJ 

o 

G 

•G 

r Si 

5 

87 Dog. 

86| Deg. 

86i 

Deg. 

86^ Deg. 

i 

ct 

Vj 

p ' 



























































































TRAVERSE TAI5LK. 


9 



51 50.93 

52 51.93 

53 52.93 

54 53.S3 

55 54.92 

56 55.92 


2.67 

O »7o 

2.77 

2.83 

2.88 

2.93 


50.92 
51 .92 

62.91 

53.91 

54.91 

55.91 



50.90 

51.90 

52.90 

53.90 
!54.90 


il 

56.92 

1 2.98 

56.91 

3.23 

|56.89 

| 3.48 

58 

57.92 

3.04 

!57.91 

3.29 

57.89 

I 3.54 

59 

58.92 

3.09 

58.91 

3.34 

58.89 

3.60 

SO 

59.92 

| 3.14 

j 59.90 

3.40 

!59.89 

3.66 

6 I 

60.92 

i 3-19 

60.90 

3.46 

160.89 

| 3.72 

62 

61 .92 

3.24 

i! 61.90 

3.51 

i 61.88 

3.79 

63 

64 

62.91 

3.30 

' 62.90 

3.57 

i62.88 

3.85 

63.91 

3.35 

j 63.90 

3.63 

63.88 

3.91 

65 

64.91 

3.40 

|64.90 

3.69 

64.88 

3.97 

66 

65.91 

3.45 

I65.89 

3.74 

!65.88 

4.03 

07 

66.91 

3.51 

66.89 

3.80 

;66.88 

4 -09 

68 

j67.91 

3.56 

67.89 

3.86 

67.87 

4.15 

69 

68.91 

3.61 

68.89 

3.91 

!68.87 

4 .21 

70 

69.90 

3.66 

; 69.89 

3.97 

|69.87 

4.27 

71 

;70.90 

3.72 

70.89 

4.03 

i70.87 

1 4.33 

72 

|71.90 

3.77 

71.88 

4.08 

1 71.87 

4.40 

73 

72.90 

3.82 

72.88 

4. 14 

! 72.86 

i 4.46 

74 

73.90 

3.87 

73.88 

4.20 

73.86 

i 4.52 

75 

74.90 

3.93 

74.88 

4.25 

74.86 

4.58 

76 

75.90 

3.98 

75.88 

4.31 

75.86 

4.64 

77 

76.89 

4.03 

76.88 

4.37 

76.86 

4.70 

78 

77.89 

4.08 

77.87 

4.42 

77.85 

4.76 

79 

- 78.89 

4.13 

78.87 

4.48 

78.85 

4.82 

80 

79.89 

4.19 

79.87 

4.54 

79.85 

4.88 

81 

80.89 

4.24 

80.87 

4.59 

80.85 

4.94 

82 

81.89 

4.29 

81.87 

4.65 

81.85 

5.01 

83 

82.89 

4.34 

82.87 

4.71 

82.85 

5.07 

84 

83.88 

4.40 I 

83.86 

4-76 

83.84 

5.13 

85 

84.88 

4.45 

84.86 

4 .82 

84.84 

5.19 

86 

85.88 

4.50 

85.86 

4-88 

I 85.84 

5.25 

8 7 

86.88 

4.55 

86.86 

4.93 

86.84 

5.31 

88 

87.88 

4.61 

87.86! 

4.99 

87.84 

5.37 

89 

88.88 

4.66 

88.86 1 

5.05 

88.83 

5.43 

90 

89.88 

4.71 

89.86 

5.10 

89.83 

5.49 

91 

90.88 j 

4.76 

90.85 

5.16 

90.83j 

5.56 

92 

91.87 | 

4.81 

91.85 

5.22 

91 .83 

5.62 

93 

92.87 

4.87 

92.85 

5.27 

92.83 

5.68 

94 

93.87 

4.92 

93.85 

5.33 

93.82 

5.74 

95 

94.87 

4.97 

94.85 

5.39 

94.82 

5.80 

96 

95.87 

5.02 

95.85 

5.44 

95.82 

5.86 

97 

96.87 j 

5.08 

96.84 

5 50 ! 

96.82 

5.92 

98 

97.87 

5.13 

97.84 

5.56 1 

97.82 

5.98 

99 

98.86 

5.18 

98.84 

5.61 

98.82 

6.04 

100 

99.86 

5.23 

99.84 

5.67 

99.81 

6.10 

6 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

£ i 

•- 1 
Q | 

1 

87 Deg. 

861 Deg. 

83'- Deg. i 
• 

I 


Cl 

Lat. 

Deg. 

Dep. 

O 
>- • 

c r. 

e“* 

p 

a 

a 

CD 

! Ti 
52 
, - F >3 

54 

55 

56 

57 

58 
! 59 

i 60 

50.89 
r 51.89 

52.89 

53.88 
i 54.88 
; 55.88 

56.88 
. 57.88 
j 58.87 

1 59.87 

i 60.87 
! 61.87 
! 62.87 
j 63.86 

1 64.86 
! 65.86 

l| 66.86 

67.85 

68.85 

69.85 

3.34 
• 3.40 
3.47 
3.53 
3.60 
3.66 
3 73 

1 3.79 

1 3.86 
3.92 

3.99 
4.05 
4.12 
4.19 
4.25 
4.32 
4.38 
4.45 
4.51 
4.58 

6 J 
62 
S3 
| 64 

65 

66 

67 

68 

69 

70 

70.85 

4.64 

71 

71.85 

4.71 

72 

72.84 

4.77 

73 

73.84 

4.84 

74 

74.84 

4.91 

75 

75.84 

4.97 

76 

76.84 

5.04 

77 

77.83 

5.10 

78 

78.83 

5.17 

79 

79.83 

5.23 

80 

80.83 

5.30 

81 

81.82 

5.36 

82 

82.82 

5.43 

83 

83.82 

5.49 

84 

84.82 

5.56 

85 

85.82 

5.62 

86 

86.81 

5.69 

87 

87.81 

5.76 

88 

88.81 

5.82 

89 

!89.81 

5.89 

90 

i 90.81 

5.95 

91 

91.80 

6.02 

92 

1 92.80 

6.08 

93 

93.80 

6.15 

94 

94.80 

6.21 

95 

95.79 

6.28 

96 

96.79 

6.34 

97 

97.79 

6.41 

98 

98.79 

6.47 

99 

99.79 

6.54 

100 

Dep. j 

Lat. 

6 

o 

I 


a 



d 

861 Deg. 

. — « 

£3 


















































































































10 


TRAVEKSE TABLE. 


Distance. 

j 

4 Deg. 

4} Deg. 

4-2 Deg. 

4| Deg. 

Distance.! 

( 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. J 

Lat. 

Dep. 

1 

1.00 

0.07 

1.00 

0.07 

1.00 

0.08 

1.00 

0.08 

1 

’ 2 

2.00 

0.14 

1.99 

0.15 

1.99 

0.16 

1.99 

0.17 

2 

3 i 

2.99 

0.21 

2.99 

0.22 

2.99 

0.24 

2.99 l 

0.25 

3 

4 

3.99 

0.28 

3.99 

0.30 

3.99 

0.31 

3.98 | 

0.33 

4 

5 ! 

4.99 

0.35 

4.99 

0.37 

4.98 

0.39 

4.98 

0.41 

5 

6 i 

5.99 

0.42 

5.98 

0.44 

5.98 

0.47 

5.98 

0.50 

6 


6.98 

0.49 

6.98 

0.52 

6.98 

0.55 

6.97 ; 

0.58 

7 

8 | 

7.98 

0.56 

7.98 

0.59 

7.98 

0.63 

7.97 

0.66 

8 

9 

8.98 

0.63 

8.98 

0.67 

8.97 

0.71 

8.97 

0.75 

9 

10 

9.98 

0.70 

9.97 

0.74 

9.97 

0.78 

9.97 

0.83 

10 

11 

10.97 

0.77 

10.97" 

0.82 

10.97 

0.86 

10.96 

0.91 

11 

12 

11.97 

0.84 

11.97 

0.89 

11.96 

0.94 | 

11.96 

0.99 

12 

13 

12.97 

0.91 

12.96 

0.96 

12.96 

1.02 

12.96 | 

1.08 

J3 

14 

13.97 

0.98 

13.96 

1.04 

13.96 

1.10 

13.95 

1.16 

14 

15 

14.96 

1.05 

14.96 

1.11 

14.95 

1.18 

14.95 

1.24 

15 

16 

15.96 

1.12 

15.96 

1.19 

15.95 

1.26 

15.95 

1.32 

) 6 

17 

16.96 

1.19 

16.95 

1.26 

16.95 

1.33 

16.94 

1.41 

17 

18 

17.96 

1.26 

17.95 

1.33 

17.94 

1.41 

17.94 

1.49 

18 

19 

18.95 

1.33 

18.95 

1.40 

18.94 

1.49 

18.93 

1.57 

19 

20 

19.95 

1.40 

19.95 

1.48 

19.94 

1.57 

19.93 

1.66 

20 

21 

20.95 

1.46 

20.94 

1.56 

20.94 

1.65 

20.93 

1.74 

21 

22 

21.95 

1.53 

21.94 

1.63 

21.93 

1.73 

21.82 

i. 82 

22 

23 

22.94 

1.60 

22.94 

1.70 

22.93 

1.80 

22.92 

1.90 

23 

24 

23.94 

1.67 

23.93 

1.78 

23.93 

1.88 

23.92 

1.99 

24 

25 

24.94 

1.74 

24.93 

1.85 

24.92 

1.96 

24.91 

2.07 

25 

20 

25.94 

1.81 

25.93 

1.93 

25.92 

2.04 

25.91 

2.15 

26 

27 

20.93 

1.88 

26.93 

2.00 

26.92 

2.12 

26.91 

2.24 

27 

28 

27.93 

1.95 

27.92 

2.08 

27.91 

2.20 

27.90 

2.32 

28 

29 

28.93 

2.02 

28.92 

2.15 

28.91 

2.28 

28.90 

2.40 

29 

30 

29.93 

2.09 

29.92 

o 0*7 

• Ar/V 

29.91 

2.35 

I 29.90 

2.48 

30 

31 

30.92 

2.16 

30.91 

2.30 

30.90 

2.43 

30.89 

2.57 

31 

32 

31.92 

2.23 

31.91 

2.37 

31.90 

2.51 

i31.89 

2.65 

32 

33 

32.92 

2.30 

32.91 

2.45 

32.90 

2.59 

32.89 

2.73 

33 

34 

33.92 

2.37 

33.91 

2.52 

j 33.90 

2.67 

33.88 

2.82 

34 

35 

i34.91 

2.44 

34.90 

2.59 

I 34.89 

2.75 

34.88 

2.90 

35 

36 

35.91 

1 2.51 

35.90 

2.67 

35.89 

2.82 

35.88 

2.98 

36 

37 

36.91 

2.58 

36.90 

2.74 

36.89 

2.90 

36.87 

3.06 

37 

38 

37.91 

2.65 

37.90 

2.82 

37.88 

2.98 

37.87 

3.15 

38 

30 

38.90 

I 2.72 

38.89 

2.89 

38.88 

3.06 

38.87 

3.23 

39 

40 

39.90 

2.79 

39.89 

2.96 

39.88 

3.14 

39.86 

3.31 

40 

41 

40.90 

1 2.80 

40.89 

3.04 

40.87 

3.22 

40.86 

3.40 

41 

42 

141.90 

2.93 

41.88 

3.11 

41.87 

3.30 

41.86 

3.48 

42 

43 

j42.00 

3.00 

42.88 

3.L9 

42.87 

3.37 

42.85 

3.56 

43 

44 

143.89 

3.07 

43.88 

3.26 

43.86 

3.45 

43.85 

3.64 

44 

45 

44.89 

! 3.14 

44.88 

3.33 

44.86 

3.53 

44.85 

3.73 

45 

46 

45.89 

1 3.21 

45.87 

3.41 

45.86 

3.61 

45.84 

3.81 

46 

47 

46.89 

3.28 

46.87 

3.48 

46.86 

3.69 

46.84 

3.89 

47 

48 

47.88 

3.35 

47.87 

3.56 

47.85 

3.77 

47.84 

1 3.97 

48 

49 

48.88 

3.42 

48.87 

3.63 

48.85 

3.84 

48.83 

4.06 

49) 

50 

49.88 3.49 

49.86 

3.71 

49.85 

3.92 

49.83 

! 4.14 

50 

• 

© 

c 

£ 

• fH 

P 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

| Lat. 

© 

o 

c 

86 Deg. 

85f Deg. 

85-| Dog. 

85J Deg. 

ci 

«-> 

C/l 

P 







































































































































TRAVERSE TABLE. 


11 


o 

cn* 

P 

4 Dog. 

4} Deg. 

4£ Deg. 

4| Dog. 

Distance. 

3 

O 

ra 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.88 

3.56 

50.86 

3.78 

50.84 

4.00 

50.82 

4.22 

51 

52 

51.87 

3.63 

51.86 

3.85 

51.84 

4.08 

51.82 

4.31 

52 

53 

52.87 

3.70 

52.85 

3.93 

52.84 

4.16 

52.82 

4.39 

53 

54 

53.87 

3.77 

53.85 

4.00 

53.83 

4.24 

53.81 

4.47 

54 

55 

54.87 

3.84 

54.85 

4.08 

54.83 

4.32 

54.81 

4-55 

55 

5B 

55.86 

3.91 

55.85 

4.15 

55.83 

4.39 

55.81 

4.64 

56 

57 

56.86 

3.98 

56.84 

4.22 

56.82 

4.47 

56.80 

4.72 

57 

58 

57.86 

4.05 

57.84 

4.30 

57.82 

4.55 

57 80 

4.80 

58 

1 59 

58.86 

4.12 

58.84 

4.37 

58.82 

4.63 

58.80 

4.89 

59 

60 

59.85 

4.19 

59.84 

4.45 

59.82 

4.71 

59.79 

4.97 

60 

61 

60.85 

4.26 

60.83 

4.52 

60.81 

4.79 

60.79 

5.05 

61 

62 

61.85 

4.32 

i61.83 
j 62.83 

4.59 

61.81 

4.86 

61.79 

5.13 

62 

63 

62.85 

4.39 

4.67 

62.81 

4.94 

62.78 

5.22 

63 

64 

63.84 

4.46 

:63.82 

4.74 

63.80 

5.02 

03 .78 

5.30 

64 

65 

64.84 

4.53 

64.82 

4.82 

64.80 

5.10 

64.78 

5.38 

65 

66 

65.84 

4.60 

65.82 

4.89 

65.80 

5.18 

65.77 

5.47 

66 

67 

66.84 

4.67 

66.82 

4.97 

66.79 

5.28 

66.77 

5.55 

67 

68 

67.83 

4.74 

67.81 

5.04 

67.79 

5.34 

67.77 

5.63 

68 

69 

68.83 

4.81 

68.81 

5.11 

68.79 

5.41 

68.76 

5.71 

69 

70 

69.83 

4.88 

69.81 

5.19 

69.78 

5.49 

69.76 

5.80 

70 

7~1 

70.83 

4.95 

70.80 

5.26 

70.78 

5.57 

70.76 

5.88 

71 

72 

71.82 

5.02 

71.80 

5.34 

71.78 

5.65 

71.75 

5.96 

72 

73 

72.82 

5.09 

72. SO 

5.41 

72.77 

5.73 

72.75 

6.04 

73 

74 

73.82 

5.16 

1 73.80 

5.48 

73.77 

5.81 

73.75 

6.13 

74 

75 

74.82 

5.23 

!74.79 

5.56 

74.77 

5.88 

74.74 

6.21 

75 

76 

75.81 

5.30 

j 75.79 

5.63 

75.77 

5.96 

75.74 

6.29 

76 

7 / 

76.81 

5.37 

!76.79 

5.71 

76.76 

6.04 

76.74 

6.38 

77 

78 

77.81 

5.44 

77.79 

5.78 

77.76 

6.12 

77.73 

6.46 

78 

79 

78.81 

5.51 

78.78 

5.85 

78.76 

6.20 

78.73 

6.54 

79 

80 

79.81 

5.58 

79.78 

5.93 

79.75 

6.28 

79.73 

6.62 

80 

81 

80.80 

5.65 

'80.78 

6.00 

80.75 

6.36 

80.72 

6.71 

81 

82 

81.80 

5.72 

81.78 

6.08 

81.75 

6.43 

81.72 

6.79 

82 

83 

82.80 

5.79 

82.77 

6.15 

82.74 

6.51 

82.71 

6.87 

83 

84 

83.80 

5.86 

183.77 

6.23 

83.74 

6.59 

83.71 

6.96 

84 

85 

84.79 

5.93 

84.77 

6.30 

84.74 

6.67 

84.71 

7.04 

85 

86 

85.79 

6.00 

85.76 

6.37 

85.73 

6.75 

85.70 

7.12 

86 

87 

86.79 

6.07 

1 86.76 

6.45 

86.73 

6.83 

86.70 

7.20 

87 

88 

87.79 

6.14 

;87.76 

6.52 

87.73 

6.90 

87.70 

7.29 

88 

89 

88.78 

6.21 

88.76 

0.60 

88.73 

6.98 

88.70 

7.37 

89 

90 

89.78 

6.28 

89.75 

6.67 

89.72 

7.06 

89.69 

7.45 

90 

91 

90.78 

6.35 1 

90.75 

6.74 

90.72 

7.14 

90.69 

7.54 

91 

92 

91.78 

6.42 | 

91.75 

6.82 

91.72 

7.22 

91.68 

7.62 

92 

93 

92.77 

6.49 

92.74 

6.89 

92.71 

7.30 

92.68 

7.70 

93 

94 

93.77 

6.56 

93.74 

6.97 j 

93.71 

7.38 

93.68 

7.78 

94 

95 

94.77 1 

6.63 

94.74 

7.04 j 

94.71 

7.45 

94.67 

7.87 

95 

96 

95.77 I 

6.70 

95.74 

7.11 

95.70 

7.53 

95.67 

7.95 

96 

97| 

96.76 ! 

G. 77 

96.73 

7.19 I 

96.70 

7.61 

96.67 

8.03 

97 

98 I 

97.76 | 

6.84 

97.73 

7.26 ! 

97.70 

7.69 

97.66 

8.12 

98 

99 

98.76 : 

6.91 

98.73 

7.34 |i 

98.69 

7.77 

98.66 

8.20 

99 

100 

99.76 | 

6.98 

99.73 

7.41 

99.69 

7.85 

99.66 

8.28 

100 

a! 

u 

c 

j 

Don. 

1 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lcit* 

Dep. 

Lat. j 

6 

o 

c 

rt 

w 

'•s 

86 Deg. 

85 f De?. ! 

851 Deg. 

85} Deg. 

C* 

*1 


I'JVMtxaaanMM — .. . - r mu ... i i i - - ^ 









































































































12 


TRAVERSE TABLE. 


Distance. 

5 Deg. 

5} Deg. 

5^ Deg. 

5f Deg. 

* 

cn 

c* 

p 

a 

Lat. 

DeD. 

£ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

1.00 

0.09 

1.00 

0.09 

1.00 

0.10 

0.99 

0.10 

if 

2 

1.99 

0.17 

1.99 

0.18 

1.99 

0.19 

1.99 

0.20 

S) | 

/■* s 

31 

2.99 

0.26 

2.99 

0.27 

2.99 

0.29 

2.98 

0.30 


4i 

3.98 

0.35 1 

3.98 

0.37 

3.98 

0.38 

3.98 

0.40 

4 \ 

5 

4.98 

0.44 

4.98 

0.46 

4.98 

0.48 

4.97 

0.50 | 

5 i 

6 

5.98 

0.52 

5.97 

0.55 

5.97 

0.58 

5.97 

0.60 

6 i 

7 

6.97 

0.61 

6.97 

0.64 

6.97 

0.67 

6.96 

0.70 


8 i 

7.97 

0.70 

7.97 

0.73 

7.96 

0.76 

7.96 

0.80 

Si 

9 

8.97 

0.78 

8.96 

0.82 

8 96 

0.86 

8.95 

0.90 

9 ! 

10 j 

9.96 

0.87 

9.96 

0.92 

9.95 

0.96 

9.95 

1.00 

10 

11 i 

10.96j 

0.96 I 

10.95 

1.01 

10.95 

1.05 

10.94 

1.10 

11 

12 

11.95 

1.05 

1 1.95 

1.10 

11.94 

1.15 

11.94 

1.20 

12 

13 

12.95 

1.13 

12.95 

1.19 j 

12.94 

1.25 

12.93 

1.30 

13 

14 

13.95 

1.22 ! 

13.94 

1.28 

13.94 

1.34 

13.93 

1.40 

14 

15 

14.94 

1.31 ! 

14.94 

1.37 

14.93 

1.44 

14.92 

1.50 

l *L 

16 

15.94 

1.39 

15.93 

1.46 

15.93 

1.53 

15.92 

1.60 

lt> 

17 

16.94 

1.48 

16.93 

1.56 

16.92 

1.63 1 

16.91 

1.70 

17 

18 

17.93 

1.57 

17.92 

1.65 

17.92 

1.73 

17.91 

1.80 

18 i 

19 

18.93 

1.66 I 

18.92 

1.74 

18.91 

1.82 1 

18.90 

1.90 

19 

20 

19.92 

1.74 

19.92 

1.83 

19.91 

1.92 

19.90 

2.00 

20 

21 

20.92 

1.83 

20.91 

1.92 

20.90 

3.01 

20.89 

2.10 

21 

22 

21.92 

1.92 i 

21.91 

2.01 

21.90 

2.11 ! 

21.89 

2.20 

22 

23 

22.91 

2.00 | 

22.90 

2.10 

22.89 

2.20 

22.88 

2.30 

23 

24 

23.91 

2.09 i 

23.90 

2.20 

23.89 

2.30 

23.88 

2.40 

24 

25 

24.90 

2.18 

24.90 

2.29 

24.88 

2.40 

24.87 

2.50 

25 

26 

25.90 

2.27 

|25.89 

2.38 

25.88 

2.49 

25.87 

2.60 

26 

27 

26.90 

2.35 

i26.89 

2.47 

26.88 

2.59 

26.86 

2.71 

27 

28 

27.89 

2.44 

27.88 

2.56 

27.87 

2.68 

27.86 

2.81 

28 

29 

28.89 

2.53 

28.88 

2.65 

28.87 

2.78 

28.85 

2.91 

29 

30 

29.89 

2.61 

I 29.87 

2.7S 

29.86 

2.88 j 

29.85 

3.01 

30 

' 31 

30.88 

2.70 

30.87 

2.84 

!30.86 

2.97 1 

30.84 

3.11 

31 

32 

31.86 

2.79 

31.87 

2.93 

|31.85 

3.07 

31.84 

3.21 

32 

33 

32.87 

2.88 

32.86 

3.02 

1 32.85 

3.16 

32.83 

3.31 

33 

34 

33.87 

2.90 

33.86 

3.11 

33.84 

3.26 

33.83 

3.41 

34 

35 

34.87 

3.05 

!34.85 

3.20 

34.84 

3.35 

34.82 

3.51 

35 

36 

35.86 

3.14 

|35.85 

3.29 

35.83 

3.45 

35.82 

3.61 

36 

37 

36.86 

3.22 

|36.84 

3.39 

36.83 

3.55 

36.81 

3.71 

37 

38 

37.86 

3.31 

!37.84 

3.48 

37.83 

3.64 

37.81 

3,81 

38 

39 

38.85 

3.40 

33.84 

3.57 

38.82 

3.74 

38.80 

3.91 

39 

40 

39.85 

3.49 

39.83 

3.66 

39.82 

3.83 

39.80 

4.01 

40 

41 

40.84 

3.57 

40.83 

3.75 

40.81 

3.93 

40.79 

4.11 

41 

42 

41.84 

3.66 

41.82 

3.84 

41.81 

4.03 

41.79 

4.21 

42 

43 

42.84 

3.75 

42.82 

3.93 

42.80 

4.12 

42.78 

4.31 

43 

44 

43.83 

3.83 

43.82 

4.03 

43.80 

4.22 

43.78 

4. 41 

44 

45 

'44.83 

3.92 

44.81 

4.12 

44.79 

4.31 

44.77 

4 51 

45 

46 

45.82 

4.01 

45.81 

4.21 

45.79 

4.41 

45.77 

4.61 

46 

47 

46.82 

4.10 

46.80 

4.30 

46.78 

4.50 

46.76 

4.71 

47 

48 

47.82 

4.18 

47.80 

4.39 

47.78 

4.60 

47.76 

4.81 

48 

49 

48.81 

4.27 

48,79 

4.48 

48.77 

4.*70 

48.75 

4.91 

49 

50 

49.81 

4.36 

49.79 

4.58 

49.77 

4.79 

49.75 

5.01 

50 

Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

t 

Distance. 1 

85 Deg. 

84| Deg. 

{ B4| Deg. 

1 

84} Deg. 








































































































































TRAVEUSE TABLE. 


13 


f—4 

W 
►«- • 
CD 
c+ 

P 

5 Deg. 

5\ Deg. 

6 £ 

Deg. 

5| Deg, 

i e 

1 CD 

1 P 

1 3 

: O 

1 CD 

» 

o 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

• 

Dep. 

Lat. 

| Dep. 

51 

50.81 

4.44 

50.79 

4.67 

50.77 

4.89 

50.74 

I 5.11 

51 

52 

51.80 

4.53 

51.78 

4.76 

51.76 

4.98 

51.74 

5.21 

52 

53 

52.80 

4.62 

52.78 

4.85 

52.76 

5.08 

52.73 

5.31 

58 

54 

53.79 

4.71 

53.77 

4.94 

53.75 

5.18 

53.73 

5.41 

54 

55 

51.79 

4.79 

54.77 

5.03 

54.75 

5.27 

54.72 

5.51 

55 

56 

55.79 

4.88 

55 . 77 

5.12 

55.74 

5.37 

55.72 

5.61 

56 

57 

56.78 

4.97 

56 . 76 

5.22 

1 56 . 74 

5.46 

.56.71 

5.71 

57 

58 

57.78 

5.06 

57 . 76 

5.31 

57.73 

5.56 

57.71 

5.81 

58 

59 

58.78 

5.14 

58.75 

5.40 

158.73 

5.65 

58.70 

5.91 

59 

60 

59.77 

5.23 

59.75 

5.49 

59.72 

5.75 

59.70 

6.01 

| 60 

61 

60.77 

5.32 

60 . 74 

5.58 

60.72 

5.85 

60.69 

6.11 

i 61 

62 

61.76 

5.40 

61.74 

5 . 67 

61.71 

5.94 

61.69 

6.21 

62 

63 

62 . 76 

5.49 

62 . 74 

5.76 

62 . 71 

6.04 

62.68 

6.31 

63 

64 

63.76 

5.58 

63 . 73 

5 . 86 

63.71 

6.13 

63.68 

6.41 

64 

65 

64.75 

5.67 

64.73 

5.95 

64.70 

6.23 

64.67 

6.51 

65 

G6 

65.75 

5.75 

65 . 72 

6.04 

65 . 70 

6.33 

65.67 

6.61 

66 

67 

66.75 

5.84 

66.72 

6.13 

66 . 69 

6.42 

66.66 

6.71 

67 

68 

67.74 

5.93 

67.71 

6.22 

67.69 

6.52 

67.66 

6.81 

68 

69 

68.74 

6.01 

68.71 

6.31 

68.68 

6.61 

68 . 65 

6.91 

69 

70 

69.73 

6.10 

69.71 

6.41 

69.68 

6.71 

69.65 

7.01 

70 

71 

70.73 

6.19 

70 . 70 

6.50 

70.67 

6.81 

70.64 

7.11 

71 

73 

71.73 

6.28 

71.70 

6.59 

71.67 

6.90 

71.64 

7.21 

72 

73 

72 . 72 

6.36 

72.69 

6.68 

72.66 

7.00 

72.63 

7.31 

73 

7 4 

73 . 72 

6.45 

73.69 

6.77 ( 

73.66 

7.09 

73 . 63 

7.41 

74 

75 

74.71 

6.54 

74.69 

6.86 

74.65 

7.19 

74.62 

7.51 

75 

76 

75.71 

6.62 

75.68 

6.95 

75.65 

7.28 

75.62 

7.61 

76 

77 

76.71 

6.71 

76.68 

7.05 

76.65 

7.38 

76.61 

7.71 

77 

78 

77.70 

6.80 

77.67 

7.14 

77.64 

7.48 

77.61 

7.81 

78 

79 1 

79 

78.70 

6.89 

78.67 

7.23 

78.64 

7.57 

78.60 

7.91 

80 

79.70 

6.97 

79.66 

7.32 

79.65 

7.67 

79.60 

8.02 

80 

81 

80.69 

7.06 

80.66 

7.41 

80.63 

7.76 

80.59 

8.12 

81 

82 

81.69 

7.15 

81.66 

7.50 

81.62 

7.86 

81.59 

8.22 

82 

83 

82.68 

7.23 

82.65 

7.59 

82.62 

7.96 

82.58 

8.32 

83 

84 

83.68 

7.32 

83.65 

7.69 

83.61 

8.05 

83.58 

8.42 

84 

85 

84.68 

7.41 

84.64 

7.78 

84.61 

8.15 

84.57 

8.52 

85 

86 

85.67 

7.50 

85.64 

7.87 

85.60 

8.24 

85.57 

8.62 

86 

87 

86.67 

7.58 

86.64 

7.96 

86.60 

8.34 

86.56 

8.72 

87 

88 

87.67 

7.67 

87.63 

8.05 

87.59 

8.43 

87.56 

8.82 

88 

89 

88.66 

7.76 

88.63 

8.14 

88.59 

8.53 

88.55 

8.92 

89 

90 

89.66 

7.84 

89.62 

8.24 

89.59 

8.63 

89.55 

9.02 

90 

91 

90.65 

7.93 

90.62 

8.33 

90.58 

8.72 

90.54 

9.12 

91 

92 

91.65 

8.02 

91.61 

8.42 

91.58 

8.82 

91.54 

9.22 

92 

93 

92.65 

8.11 

92.61 

8.51 

92.57 

8.91 

92.53 

9.32 

93 

94 

93.64 

8.19 

93.61 

8.60 

93.57 

9.01 

93.53 

9.42 

94 

1 95 

94.64 

8.28 

94.60 

8.69 

94.56 

9.11 

94.52 

9.52 

95 

96 

95.63 

8.37 

95.60 

8.78 

95.56 

9.20 

95.52 

9.62 

96 

97 

96.63 

8.45 

96.59 

8.88 

96.55 

9.30 

96.51 

9.72 

97 

98 

97.63 

8.54 

97.59 

8.97 

97.55 

9.39 

97.51 

9.82 

98 

99 

98.62 

8.63 

98.59 

9.06 

98.54 

9.49 

98.50 

9.92 

99 

100 

99.62 

8.72 

99.58 

9.15 

99.54 

9.58 

99.50 

10.02 

100 

d 

§ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

©" 

I 

1 

«-<> 

y) 

5 1 
' 

85 Deg. 

84J Deg. 

84| Deg. 

84£ Deg 

cd 

«-> 

W 

• 

°j 


20 


‘i 






















































































































14 


TRAV7RSE TABLE. 


»■ 

w 

cr^ 

p 

3 

c 

O 

* 

6 Deg. 

6i Deg. 

6| Deg. 

6| Deg. 

o 

5? 

c* 

p 

3 

o 

3 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i i 

0.99 

0. 

10 

0.99 

0.11 

0.99 

0.11 

0.99 

0.12 

I 

2 1 

1.99 

0. 

21 

1.99 

0.22 

1.99 

0.23 

1.99 

0 24 

2 

3 , 

2.98 

0. 

31 

2.98 

0.33 

2.98 1 

0.34 

2.98 

0 35 

3 

4 

3.98 

0. 

41 

3.98 

0 44 

3.97 j 

0.45 

3.97 

0,47 

4 

5 i 

4.97 

0. 

52 

4.97 

0.54 

4.97 

0.57 

4.97 

9.59 

5 

8 | 

5.97 

0. 

63 

5.96 

0.65 

5.98 i 

0.68 

5.96 

0.71 

6 

7 

6.96 

0. 

73 

6.96 

0.76 

6.96 { 

0.79 

6.95 

0.82 

7 

8 

7.96 

0. 

84 

7.95 

0.87 

7.95 

0.91 

7.94 

0.94 

9 

9 

8.95 

0. 

94 

8.95 

0.98 

8.94 

1.02 

8.94 

1.00 

9 

10 

9.95 

1. 

05 | 

9.94 

1.09 

9.94 

1.13 

9.93 

1.18 

10 

11 

10.94 

1. 

15 i 

10.93 

1.20 

10.93 

1.25 

10.92 

1.29 

11 

12 

11.93 

1 . 

25 

11.93 

1.31 

11.92 

1.36 

11.92 

1.4] 

12 

13 

12.93 

1. 

36 

12.92 

1.42 

12.92 

l. 47 1 

12.91 

1.53 

13 

14 

13.92 

1 . 

46 

13.92 

1.52 

13.91 

1.59 j 

13.90 

1.65 

14 

15 

14.92 

1. 

57 

14.91 

1.63 

14.90 

1.7<‘ 

14.90 

1.76 

15 

16 

15.91 

1. 

67 

15.90 

1.74 

15.90 

1.81 

15.89 

1.88 

16 

17 

16.91 

1. 

78 

16.90 

1.85 

16.89 

1.92 

16.88 

2 00 

17 

18 

17.90 

1 

83 

17.89 

1.96 

17.88 

2.04 

17.88 

2.12 

18 

19 

18.90 

1 

99 

18.89 

2.07 

18.88 

2.15 

18. S7 

2.23 

19 

20 

19.89 

2. 

09 

19.88 

2.18 

19.87 

2.26 

19.86 

2.35 

20 

21 

20.88 

2. 

20 

20.88 

2.29 

20.87 

2.38 

20.85 

2.47 

21 

22 

21.88 

2. 

30 

21 .87 

2.40 

21.86 

2.49 

21.85 

2.59 

oo 

A# <<«* 

23 

22.37 

2. 

40 

22.86 

2.50 

22.85 

2.60 

22.84 

2.70 

23 

24 

23.87 

2. 

51 

23.86 

2.61 

23.85 

2.72 

23.83 

2.82 

24 

25 

24.86 

2 

61 

24.85 

2.72 

24.84 

2.83 

24.83 

2.94 

25 

26 

25.86 

2 

72 

25.85 

2.83 

25.83 

2.94 

25.82 

3.06 

26 

27 

26.85 

2 

82 

26.84 

2.94 

26.83 

3.06 

26.81 

3.17 

27 

28 

27.85 

2 

93 

27.83 

3.05 

27.82 

3.17 

27.81 

3.29 

28 

29 

28.84 

3 

03 

28.83 

3.16 

28.SI 

3.28 

28.80 

3.41 

29 

30 

29.84 

3 

14 

29.82 

3.27 

29.81 

3.40 

29.79 

3.53 

30 

'31 

30.83 

3 

.24 

30.82 

3.37 

30.80 

3.51 

30.79 

3.64 

31 

32 

31 82 

3 

.34 

31.81 

3.48 

31.79 

3.62 

31.78 

3.76 

32 

33 

32.82 

3 

.45 

32.80 

3.59 

32.79 

3.74 

32.77 

3.88 

33 

34 

33.81 

3 

55 

33 30 

3.70 

33.78 

3.85 

33.76 

4.00 

3a 

35 

34.81 

3 

.66 

34.79 

3.81 

34.78 

3.96 

34.76 

4.11 

35 

36 

35.80 

3 

.76 

35.79 

3.92 

35.77 

4.08 

35.75 

4.23 

36 

37 

36.80 

3 

.87 

36.78 

4.03 

36.76 

4.19 

36.75 

4.35 

37 

38 

37.79 

3 

.97 

37.77 

4.14 

37.76 

4.30 

37.74 

4.47 

38 

39 

38.79 

4 

.08 

38.77 

4.25 

38.75 

4.41 

38.73 

4.58 

39 

40 

39.78 

4 

.18 

39.76 

4.35 

39.74 

4.53 

39.72 

4.70 

40 

41 

40.78 

4 

.29 

40.76 

4.46 

40.74 

4.64 

40.72 

4.82 

41 

42 

41.77 

4 

.39 

41.75 

4.57 

41.73 

4.76 

41.71 

4.94 

42 

43 

42.76 

4 

.49 

42.74 

4.68 

42.721 4.87 

42.70 

5.05 

43 

44 

43.76 

4 

.60 

43.74 

4.79 

43.72 

4.98 

43.70 

5.17 

44 

45 

44.75 

1 4 

.70 

44.73 

4.90 

44.71 

5.09 

44.69 

5.29 

! 45 

46 

45.75 

! 4 

.81 

45.73 

5.01 

45.70 

5.21 

45.68 

5.41 

1 46 

47 

46.74 

4 

.91 

46.72 

5.12 

46.70 

5.32 

46.67 

5 52 

47 

48 

47.74 

i 5 

.02 

47.71 

5.23 

47.69 

5.43 

47.67 

5.64 

48 

49 

48.73 

5 

.12 

48.71 

5.34 

48.69 

5.55 

48.66 

5.76 

49 

50 

49.73 

5 

.23 

49.70 

5.44 

49.68 

5.66 

49.65 

5.88 

50 

® 

O 

a 

s 

.n 

Q 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

J Lat. 

1 ' V 

1 a> 

i c 

84 Deg. 

83f Deg. 

332 

i 

Deg. 

83^ Deg. 

i 

! s* 

W 

X 

<5 































































































































TRAVERSE TABLE 


16 


c 

b-t • 

a 

c+ 

p 

6 Deg. 

6} Deg. 

6^ Deg 

6} Deg. 

O 

rr 

e**» 

g 

Zj 

a 

a 

» 

2 

o 

a 

Lat. 

Dep. 

Lat. 

Dep. 

J at. 

Dep. 

Lat. 

Dep. 

51 

50.72 

5.33 

50.70 

5.55 

50.67 

5.77 

50.65 

5.99 

51 

52 

51.72 

5.44 

51.69 

5.66 

51.67 

5-89 

51.64 

6.11 

52 

53 

52.71 

5.54 

52.63 

5.77 

52.66 

6-00 

52.63 

6.23 

53 

54 

53.70 

5.64 

53.68 

5.88 

53.65 

6.11 

53.63 

6.35 

54 

55 

54.70 

5.75 

54.67 

5.99 

54.65 

6-23 

54.62 

6.46 

55 

56 

55.69 

5.85 

55.67 

6.10 

55.64 

0-34 

55.61 

6.58 

50 

57 

56:69 

5.96 

56.63 

6.21 

56.63 

6-45 

56.60 

6.70 

57 

58 

57.68 

6.06 

57.66 

6.31 

57.63 

6 • 57 

57.60 

6.82 

58 

59 

58.68 

6.17 

j 58.65 

6.42 

58.62 

6-68 

58.59 

6.93 

59 

60 

59.67 

6.27 

59.64 

6.53 

59.61 

6 • 79 ! 

59.58 

7.05 

60 

61 

60.67 

6.38 

60.64 

6.64 

60.61 

6.91 1 

60.58 

7.17 

61 

62 

61.66 

6.48 

61.63 

6.75 

61.60 

7.02 

61.57 

7.29 

62 

63 

62.65 

6.59 

62.63 

6.86 

62.60 

7.13 I 

62.56 

7.40 

63 

64 

63.65 

6.69 

63.62 

6.97 

63.59 

7.25 

63.56 

7.52 

64 

65 

64.64 

6.79 

64.61 

7.08 

64.58 

7.36 

64.55 

7.64 

65 

66 

65.64 

6.90 

65.61 

7.19 

65.58 

7.47 

65.54 

7.76 

66 

67 

66.63 

7.00 

66.60 

7.29 

66.57 

7 58 

66.54 

7.88 

67 

68 

67.63 

7.11 

67.60 

7.40 

67.56 

7.70 

67.53 

7.99 

68 

69 

68.62 

7.21 

68.59 

7.51 

68.56 

7.81 

68.52 

8.11 

69 

70 

69.62 

7.32 

69.58 

7.62 

69.55 

7.92 

69.51 

8.23 

70 

71 

70.61 

7.42 

70.58 

7.73 

70.54 

8.04 

70.51 

8.35 

71 

72 

71.61 

7.53 

71.57 

7.84 

71.54 

8.15 

71.50 

8.46 

72 

73 

72.60 

7.63 

72.57 

7.95 

72.53 

8.26 

72.49 

8.58 

73 

74 

73.59 

7.74 

73.50 

8.06 

73.52 

8.38 

73.49 

8.70 

74 

75 

74.59 

7.84 

74.55 

8.17 

74.52 

8.49 

74.48 

8.82 

75 

76 

75.58 

7.94 

75.55 

8.27 

75.51 

8.60 

75.47 

8.93 

76 

77 

76.58 

8.05 

76.54 

8.38 

76.51 

8.72 

76.47 

9.05 

77 

78 

77.57 

8.15 

77.54 

8.49 

77.50 

8.83 

i77.46 

9.17 

78 

79 

78.57 

8.26 

78.53 

8.60 

78.49 

8.94 

178.45 

9.29 

79 

80 

79.56 

8.36 

79.53 

8.71 

79.49 

9.06 

79.45 

9.40 

80 

81 

80.56 

8.47 

80.52 

8.82 

80.48 

9.17 

80.44 

9.52 

81 

82 

81.55 

8.57 

81.51 

8.93 

81.47 

9.28 

81.43 

9.64 

82 

83 

82.55 

8.68 

82.51 

9.04 

82.47 

9.40 

82.42 

9.76 

83 

84 

83.54 

8.78 

83.50 

9.14 

83.46 

9.51 

83.42 

9.87 

84 

85 

84.53 

8.88 

84.50 

9.25 

84.45 

9.62 

84.41 

9.99 

85 

86 

85.53 

8.99 

85.49 

9.36 

85.45 

9.74 

85.40 

10.11 

86 

87 

86.52 

9.09 

86.48 

9.47 

86.44 

9.85 

86.40 

10.23 

87 

88 

87.52 

9.20 

87.48 

9.58 

87.43 

9.96 

87.39 

10.34 

88 

89 

88.51 

9.30 

88.47 

9.69 

88.43 

10.08 

88.38 

10.46 

89 

90 

89.51 

9.41 

89.47 

9.80 

89.42 

10.19 

|89.38 

10.58 

90 

91 

90.50 

9.51 

90.46 

9.91 

90.42 

10.30 

i90.37 

10.70 

91 

92 

91.50 

9.62 

91.45 

10.02 

91.41 

10.41 

91.3G 

10.81 

92 

93 

92.49 

9.72 

92.45 

10.12 

92.40 

10.53 

92.36 

10.93 

93 

94 

93.49 

9.83 

93.44 

10.23 

93.40 

10.64 

93.35 

11.05 

94 

95 

94.48 

9.93 

94.44 

10.34 

94.39 

10.75 

94.34 

11.17 

95 

96 

95.47 

10.03 

95.43 

10.45 

95.38 

10.87 

95.33 

11.28 

96 

97 

96.47 

10.14 

96.42 

10.56 

96.38 

10.98 

96.33 

11.40 

97 

98 

97.46 

10.24 

97.42 

10.67 

97.37 

11.09 

87.32 

11.52 

98 

99 

98.46 

10.35 

98.41 

10.78 

98.36 

11.21 

98.31 

11.64 

99 

iOO 

99.45 

10.45 

99.41 

10.89 

99.36 

11.32 

99.31 

11.75 

100 

' £ 
o 

g 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dop. 

Lat. 

6 

c 

C3 

4* 

03 
• —« 

Q 

84 Deg. 

83f Deg. 

83| 

Deg. 

83} Deg. 

d 

'•“* i 

XL 

( 






























































































16 


I’RAVI US 13 TAKLK. 


| Distance. 

1 Deg. 

n Leg. 

7£ Deg 

7$ Deg. 

c 

V) 

c* 

P 

Lat. 1 

Dep. 

Lat. 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. 

_ 

.-5 

<5 

• 

1 

_ OT 99 " 

0.12 

0.99 

0.13 

0.99 

0.13 

0.99 

0.13 ! 

1 

2 

1.99 

0.24 

1.98 

0.25 

1.98 

0.2G 

1.98 

0.27 ! 

2 

3 

2.98 

0.37 

2.98 

0.38 

2.97 

0.39 

2.97 

0.40 

3 

4 

3.97 

0.49 

3.97 

0.50 

3.97 

0.52 

3.96 

0.54 

4 

5 

4.96 

0.61 

4.96 

0.63 

4.96 

0.65 

4.95 

0.67 

5 

6 

5.96 

0.73 

5.95 

0.76 

5.95 

0.78 

5.95 

0.81 

6 

7 

6.95 

0.85 

6.94 

0.88 

6.94 

0.91 

6.94 

0.94 

7 

8 

7.94 

0.97 

7.94 

1.01 

7.93 

1.04 

7.93 

1.08 

8 

9 

8.93 

1.10 

8.93 

1.14 

8.92 

1.17 

8.92 

1.21 ! 

9 

10 

9.93 

1.22 

9.92 

1.26 

9.91 

1.31 

9.91 

1.35 

10 

11 

10.92 

1.34 

10.91 

1.39 

10.91 

1.44 

10.90 

1.48 

11 

12 

11.91 

1.46 

11.90 

1.51 

11.90 

1.57 

11.89 

1.62 

12 

13 

12. SO 

1.58 

12.90 

1.64 

12.89 

1.70 

12.88 

1.75 

13 

14 

13.90 

1.71 

1.3.89 

1.77 

13.88 

1.83 

13.87 

1.89 

11 

15 

14.89 

1.83 

14.88 

1.89 

14.87 

1.96 

14.86 

2.02 

15 

16 

15.88 

1.95 

15.87 

2.02 

15.86 

2.09 

15.85 

2.16 | 

16 

17 

16.87 

2.07 

16.86 

2.15 

16.85 

2.22 

16.84 

2.29 

17 

IS 

17.87 

2.19 

17.86 

2.27 

17.85 

2.35 

17.84 

2.43 

18 

19 

18.86 

2.32 

18.85 

2.40 

18.84 

2.48 

18.83 

2.56 

19 

20 

19.85 

2.44 

19.84 

2.52 

19.83 

2.61 

19.82 

2.70 

20 

21 

20.84 

2.56 

20.83 

2.65 

20.82 

2.74 

20.81 

2. S3 

21 

22 

21.84 

2.68 

21.82 

2.78 

21.81 

2.87 

21.80 

2.97 

22 

23 

22.83 

2.80 

22.82 

2.90 

22.80 

3.00 

22.79 

3.10 

23 

24 

23.82 

2.92 

23.81 

3.03 

23.79 

3.13 

23.78 

3.24 ' 

24 

25 

24.81 

3.05 

24.80 

3.15 

24.79 

3.26 

24.77 

3.37 

25 

26 

25.81 

3.17 

25.79 

3.28 

25.78 

3.39 

25.76 

3.51 

26 

27 

26.80 

3.29 

26.78 

3.41 

26.77 

3.52 

26.75 

3.64 

27 

28 

27.79 

3.41 

27.78 

3.53 

27.76 

3.65 

27.74 

3.78 

28 

29 

28.78 

3.53 

28.77 

3.66 

28.75 

3.79 

28.74 

3.91 

29 

30 

29.78 

3.G6 

29.76 

3.79 

29.74 

3 92 

29.73 

4.05 

30 

31 

30.77 

3.78 

30.75 

3.91 

30.73 

4.05 

30.72 

4.18 

31 

32 

31.76 

3.90 

31.74 

4.04 

31.73 

4.18 

31.71 

4.32 

32 

33 

32.75 

4.02 

32.74 

4.16 

32.72 

4.31 

32.70 

4.45 

33 

34 

33.75 

4.14 

33.73 

4.29 

33.71 

4.44 

33.69 

4.58 

34 

35 

34.74 

4.27 

34 .72 

4.42 

34.70 

4.57 

34.68 

4.72 

35 

36 

35.73 

4.39 

35 .71 

4.54 

35.69 

4.70 

35.67 

4.85 

36 

37 

36.72 

4.51 

36.70 

4.67 

36.68 

4.83 

36.66 

4.99 

37 

38 

37.72 

4.63 

37.70 

4.80 

37.67 

4.96 

37.65 

5.12 

38 

39 

38.71 

4.75 

38.69 

4.92 

38.67 

5.09 

38.64 

5.26 

39 

40 

39.70 

4.67 

39.68 

5.05 

39.66 

5.22 

39.63 

5.39 

40 

41 

40.70 

5.00 

40.67 

5.17 

40.65 

5.35 

40.63 

5.53 

41 

42 

41.69 

5.12 

41.66 

5.30 

41.64 

5.48 

41.62 

5.66 

42 

43 

42.68 

5.24, 

42.66 

5.43 

42.63 

5.61 

42.61 

5.80 

43 

44 

43.67 

5.36 

43.65 

5.55 

43.62 

5.74 

43.60 

5.93 

44 

45 

44.67 

5.48 

44.64 

5.68 

44.62 

5.87 

44.59 

6.07 

45 

46 

45.66 

5.61 

45.63 

5.81 

45.61 

6.00 

45.58 

6.20 

46 

47 

46.65 

5.73 

46.62 

5.93 

46.60 

6.13 

46.57 

6.34 

47 

48 

47.64 

5.85 

47.62 

6.06 

47.59 

6.27 

147.56 

6.47 

48 

49 

48.63 

5.97 

48.61 

6.18 

48.58 

6.40 

48.55 

6.61 

49 

50 

49.63 

6.09 

49.60 

6.31 

49.57 

6.53 

49.54 

6.74 

50 

i • 

o 

3 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

O 

c 

rt 

M 

• H 

83 Deg. 

82$ Deg. 

82^ Deg. 

i 

. 82$ Deg. 

4J 

6 
• H 

Q 










































































































tkavkkse table 


17 


w 
*■"* • 

7 ) 

r+ 

P 

7 Deg. 

n Deg. 

H Deg. 

7* Deg. 

7] 

r* 

3 

O 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

2 

Ci 

O 

51 

50.62 

6.22 

50.59 

6.44 

~5 ( 56 

6.66 

50.53 

83* 

51 

52 

51.61 

6.34 

51.58 

6.56 

51.56 

6 .79 

51.53 

7.01 

52 

53 

52.60 

6.46 

52.58 

6.69 

52.55 

6.92 

52.52 

7.15 

53 

54 

1 53.60 

6.58 

53.57 

6.81 

53.54 

7.05 

53.51 

7.28 

54 

55 

54.59 

6 . 70 

54.5C 

6.94 

54.53 

7.18 

54.50 

7.42 

55 

56 

56 

55.58 

6.82 

75.55 

7.07 

55.52 

7.31 

55.49 

7.55 

57 

1 56.58 

6.95 

56.54 

7.19 

56.51 

7.44 

56.48 

7.69 

57 

58 

.57.57 

7.07 

57.54 

7.32 

57.50 

7.57 

57.47 

7.82 

58 

59 

58.56 

7.19 

58.53 

7.45 

58.50 

7.70 

58.46 

7.96 

59 

60 

59.55 

7.31 

59 . 52 

7.57 

59.49 

7.83 

59.45 

8.09 

60 

6 ] 

60.55 

7.43 

60.51 

7.70 

60.48 

7.96 

60.44 

8.23 

61 

62 

1 61.54 

7.56 

61.50 

7.82 

61.47 

8.09 

61.43 

8.36 

62 

63 

62 . 53 

7.68 

62.50 

7.95 

62.46 

8.22 

62.42 

8.50 

63 

64 

63.52 

7.80 

63.49 

8.08 

63.45 

8.35 

63.42 

8.63 

64 

65 

64.52 

7.92 

64.48 

8.20 

64.44 

8.48 

64 .41 

8 .77 

65 

66 

65.51 

8.04 

05.47 

8.33 

65.44 

8.61 

65.40 

8.90 

66 

67 

66 50 

8.17 

66.46 

8.40 

66.43 

8 . 75 

66.39 

9.04 

67 

68 

67.49 

8.29 

67.46 

8 . 58 

67.42 

8.88 

67.38 

9. 17 

68 

69 

68.49 

8.41 

68.45 

8.71 

68.41 

9.01 

68.37 

9.30 

69 

70 

69.48 

8.53 

69.44 

8.83 

69.40 

9.14 

69.36 

9.44 

70 

71 

70.47 

8.65 

70.43 

8.96 

70.39 

9.27 

70.35 

9.57 

71 

72 

71.46 

8.77 

71.42 

9.09 

71.38 

9.40 

71.34 

9.71 

72 

73 

72.46 

8.90 

72.42 

9.21 

72 38 

9.53 

72.33 

9.84 

73 

74 

73.45 

9.02 

73.41 

9.34 

73.37 

9.66 

73.32 

9.98 

74 

75 

I 74.44 

9.14 

74.40 

9.46 

74.36 

9.79 

74.31 

10.11 

75 

i 76 

1 75.43 

9.26 

75.39 

9.59 

75.35 

9.92 

75.31 

10.25 

76 

77 

76.43 

9.38 

76.38 

9.72 

76.34 

10.05 

76.30 

10.38 

77 

78 

77.42 

9.51 

77.38 

9.84 

77.33 

10. IS 

77.29 

10.52 

78 

79 

78.41 

9.63 

78.37 

9.97 

78.32 

10.31 

78 . 28 

10.65 

79 

80 

79.40 

9.75 

79.36 

10.10 

79.32 

10.44 

79 . 27 

10.79 

80 

81 

80.40 

9.87 

80.35 

10.22 

80T3T 

10.57 

80.26 

10.92 

81 

82 

81.39 

9.99 

81.34 

10.35 

81.30 

10.70 

81.25 

11.06 

82 

83 

82.38 

10.12 

82.34 

10.47 

82.29 

10.83 

82.24 

11.19 

83 

84 

83.37 

10.24 

83.33 

10.60 

83.28 

10.96 

83.23 

11.33 

84 

85 

84.37 

10.36 

84.32 

10.73 

84.27 

11.09 

84.22 

11.46 

85 

86 

85.36 

10.48 

85.31 

10.85 

85.26 

11.23 

85.21 

11.60 

86 

87 

86.35 

JO. 60 

86.30 

10.98 

86.26 

11.36 

86.21 

11 .73 

87 

88 

87.34 

10.72 

87.30 

11.11 

87.25 

11.49 

87.20 

11.87 

88 

89 

88.34 

10.85 

88.29 

11.23 

88.24 

11.62 

88.19 

12.00 

89 

90 

89.33 

10 97 

89.28 

11.36 

89.23 

11.75 

89.18 

12.14 

90 

91 

90.32 

11.09 

90.27 

11.48 

90.22 

11.88 

90.17 

12.27 


92 

91.31 

11.21 

91.26 

11.61 

91.21 

12.01 

91.16 

12.41 

92 

93 

92.31 

11.33 

92.26 

11.74 

92.20 

12.14 

92.15 

12.54 

93 

94 

93.30 

11.46 

93.25 

11.86 

93.20 

12.27 

93.14 

12.63 

94 

95 

94.29 

11.58 

94.24 

11.99 

94.19 

12.40 

94.13 

12.81 

95 

96 

95.28 

11 .70 

95.23 

12.12 

95.18 

12.53 

95.12 

12.95 

96 

97 

96.28 

11.82 

96.22 

12.24 

96.17 

12.66 

| 96.11 

13.08 

97 

98 

97.27 

11.94 

97.22 

12.37 

97.16 

12.79 

97.10 

13.22 

93 

99 

98.26 

12.07 

98.21 | 

12.49 

98.15 

12.92 

98.10 

13.35 

99 

100 | 

99.25 

12.19 

99.20 | 

12.62 

99. 14 

13.05 

99.09 

13.49 

100 

. i 

o 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

CJ 

C 1 

C& 

M 

• H 

Q 

83 Deg. 

82| Deg. 

82-| Deg. 

82:} Deg. 

d 

X 

c 










■■ — 1 - 

















































































































18 


TRAVERSE TABLE. 


o 

ST 

*-* 

8 Deg. 

8 i Deg. 

8 J Deg. 

8 | Deg. 

5 

5’ 

o- 

p 

3 

CD 

CD 

• 

Licit, 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

9 

1 

0.99" 

0.14 

0.99 

0.14 

0.99 

0.15 

0.99 

0.15 

1 

2 

1.98 

0.28 

1.98 

0.29 

1.98 

0.30 

1.98 

0.30 

2 

3 

2.97 

0.42 

2.97 

0.43 

2.97 

0.44 

2.97 

0.46 

3 

4 

3.96 

0.56 

3.96 

0.57 

3.96 

0.59 

3.95 

0.61 

1 

5 

4.95 

0.70 

4.95 

0.72 

4.95 

0.74 

4.94 

0.76 

5 

6 

5.94 

0.84 

5.94 

0.86 

5.93 

0.89 

5.93 

0 91 

6 

7 

6.93 

0.97 

6.93 

1.00 

6.92 

1.03 

6.92 

1.06 

7 

8 

7.92 

1.11 

7.92 

1.15 

7.91 

1.18 

7.91 

1 22 
1.37 

8 

9 

8.91 

1.25 

8.91 

1.29 

8.90 

1.33 

8.90 

9 

10 

9.90 

1.39 

9.90 

1.43 

9.89 

1.48 

9.88 

1.52 i 

10 

i 1 

10.89 

1.53 

10.89 

1.58 

10.88 

1.63 

10.87 

1.67 

11 

12 

11.88 

1.67 

11.88 

1.72 

11.87 

1.77 

11.86 

1.83 

12 

13 

12.87 

1.81 

12.87 

1.87 

12.86 

1.92 

12.85 

1.98 

13 

14 

13.86 

1.95 

13.86 

2.01 

13.85 

2.07 

13.84 

2.13 

14 

15 

14.85 

2.09 

14.85 

2.15 

14.84 

2.22 

14.83 

2.28 

15 

16 

15.84 

2.23 

15.84 

2.30 

15.82 

2.36 

15.SI 

2.43 

16 

17 

16.83 

2.37 

16.83 

2.44 

16.81 

2.51 

16.80 

2.59 

17 

IS 

17.82 

2.51 

17.81 

2.58 

17.80 

.2.66 

17.79 

2.74 

18 

19 

18.82 

2.64 

18.80 

2.73 

18.79 

2.81 

18.78 

2.89 

19 

20 

19.81 

2.78 

19.79 

2.87 | 

19.78 

2.96 

19.77 

3.04 

20 

21 

20.80 

2.92 

20.78 

3.01 

20.77 

3.10 

20.76 

3.19 

21 

22 

21.79 

3.06 

21.77 

3.16 

21.76 

3.25 

21.74 

3.35 

22 

23 

22.78 

3.20 

22.76 

3.30 

22.75 

3.40 

22.73 

3.50 

23 

24 

23.77 

3.34 

23.75 

3.44 

23.74 

3.55 

23.72 

3.65 

24 

25 

24.76 

3.48 

24.74 

3.59 

24.73 

3.70 

24.71 

3.80 

25 

2 G 

25.75 

3.62 

25.73 

3.73 

25.71 

3.84 

25.70 

3.96 

26 

27 

26.74 

3.76 

26.72 

3.87 

26.70 

3.99 

26.69 

4.11 

27 

28 

27.73 

3.90 | 

27.71 

4.02 

27.69 

4.14 

127.67 

4.26 

28 

29 

28.72 

4.04 

28.70 

4.16 

28.68 

4.29 

28.66 

4.41 

29 

30 

29.71 

4.18 | 

29.69 

4.30 

29.67 

4.43 

29.65 

4.56 

30 

31 

30.70 

4.31 

30.68 

4.45 

30.66 

4.58 

30.64 

4.72 

31 

32 

31.69 

4.45 

31.67 

4.59 

31.65 

4.73 

31.63 

4.87 

32 

33 

32.68 

4.59 

32.66 

4.74 

32.6; 

4.88 

32.62 

5.02 

33 

34 

33.67 

4.73 

33.65 

4.88 

33.63 

5.03 

!33.60 

5.17 

34 

35 

34.66 

4.87 

34.64 

5.02 

34.62 

5.17 

34.59 

5.32 

35 

36 

35.65 

5.01 

35.63 

5.17 

35.60 

5.32 

35.58 

5.48 

36 

37 

36.64 

5.15 

36.62 

5.31 

36.59 

5.47 

36.57 

5.63 

37 

33 

37.63 

5.29 

37.61 

5.45 

37.58 

5.62 

37.56 

5.78 

38 

39 

38.62 

5.43 

38.60 

5.60 

38.57 

5.76 

38.55 

5.93 

39 

40 

39.61 

5.57 

39-59 

5.74 

39.56 

5.91 

39.53 

6.08 

40 

41 

40.60 

5.71 

40.58 

5.88 

40.55 

6.06 

40.52 

6.24 

41 

42 

41.59 

5.85 

41.57 

6.03 

41.54 

6.21 

41.51 

6.39 

42 

43 

42.58 

5.98 

42.56 

6.17 

42.53 

6.36 

42.50 

6.54 

43 

44 

43.57 

6.12 

43.54 

6.31 

43.52 

6.50 

43.49 

6.69 

44 

45 

44.56 

6.26 

44.53 

6.46 

44.51 

6.65 

144.48 

6.85 

45 

46 

45.55 

6.40 

45.52 

6.60 

45.49 

6.80 

!45.46 

7.00 

46 

47 

46.54 

6.54 

46.51 

6.74 

46.48 

6.95 

46.45 

7.15 

47 

48 

47.53 

6.68 

47.50 

6.89 

47.47 

7.09 

47.44 

7.30 

48 

49 

48.52 

6.82 

48.49 

7.03 

48.46 

7.24 

48.43 

7.45 

49 

50 

49.51 

6.96 

49.48 

7.17 

49.45 

7.39 

49.42 

7.61 

50 

© 

s 

*■> 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

a! 

o 

c 

«-> 

w 

a 

82 Deg. 

81| Deg. 

8 l 2 L 

Deg. 

8k4 Deg. 

ci 

• —« 

P 

1 















































































































TRAVERSE TABLE 


19 


— , -.- - - 

Distance.j 

8 Deg. 

8 ^ Deg. 

8 g Deg. 

&! Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

50.50 

7.10 

50.47 

7.32 

50. LI 

7.54 

50.41 

7.76 

51 

52 

51.49 

7.24 

51.46 

7.46 

51.43 

7.69 

51.39 

7.91 

52 

53 

52.48 

7.38 

52.45 

7.61 

52.42 

7.83 

52.38 

8.06 

53 

54 

53.47 

7.52 

53.44 

7.75 

53.41 

7.98 

53.37 

8.21 

54 

55 

54.46 

7.65 

54.43 

7.89 

54.40 

8.13 

54.36 

8.37 

55 

56 

55.46 

7.79 

55.42 

8.04 

55.38 

8.28 

55.35 

8.52 

56 

57 

55.45 

7.93 

58.41 

8.18 

56.37 

8.43 

56.34 

8.67 

57 

58 

57.44 

8.07 

57.1-0 

8.32 

57.36 

8.57 

57.32 

8.82 

58 

59 

58.43 

8.21 

58.39 

8.47 

58.35 

8.72 

58.31 

8.98 

59 

60 

59.42 

8.35 

59 .38 

8.61 

59.34 

8.87 

59.30 

9.13 

60 

61 

60.41 

8.49 

60.37 

8 .75 

60.33 

9.02 

60.29 

9.28 

61 

62 

61.40 

8.63 

61.36 

8.90 

61.32 

9.16 

61.28 

9.43 

62 

63 

62.39 

8.77 

62.35 

9.04 

62.31 

9.31 

62.27 

9.58 

63 

64 

63.38 

8.91 

63.34 

9.18 

63.30 

9.46 

63.26 

9.74 

64 

65 

64.37 

9.05 

64.33 

9.33 

64.29 

9.61 

64.24 

9.89 

65 

66 

65.36 

9.19 

65.32 

9.47 

65.28 

9.76 

65.23 

10.04 

66 

67 

66.35 

9.32 

66.31 

9.61 

66.26 

S.90 

66.22 

10.19 

67 

68 

67.34 

9.46 

67.30 

9.76 

67.25 

10.05 

67.21 

10.34 

68 

69 

68.33 

9.60 

68.29 

9.90 

68.24 

10.20 

68.20 

10.50 

69 

70 

69.32 

9.74 

69.28 

10.04 

69.23 

10.35 

69.19 

10.65 

70 

71 

70.31 

9.88 

70.27 

10.19 

70.22 

10.49 

70.17 

10.80 

71 

72 

71.30 

10.02 

71.25 

10.33 

71.21 

10.64 

71.16 

10.95 

72 

73 

72.29 

10.16 

72.24 

10.47 

72.20 

10.79 

72.15 

11.10 

73 

74 

73.28 

10.30 

73.23 

10.62 

73.19 

10.94 

73.14 

11.26 

74 

75 

74.27 

10.44 

74.22 

] 0.76 

74.18 

11.09 

74.13 

11.41 

75 

76 

75.26 

10.58 

75.21 

10.91 

75.17 

11.23 

75.12 

11.56 

76 

r***/ 

t i 

76.25 

10.72 

76.20 

1 1.05 

76.15 

11.38 

76.10 

11.71 

77 

78 

77.24 

10.86 

77.19 

11.19 

77 .14 

11.53 

77.09 

11.87 

78 

79 

78.23 

10.99 

i78.18 

1 i .34 

78.13 

11.68 

78.08 

12.02 

79 

80 

79.22 

11.13 

79.17 

11.48 

79.12 

11.82 

79.07 

12.17 

80 

81 

80.21 

11.27 

80.16 

i 1.62 

80.11 

11.97 

80.06 

12.32 

81 

82 

81.20 

11.41 

181.15 

11.77 

81.10 

12.12 

81.05 

12.47 

82 

83 

82.19 

11.55 

82.14 

11.91 

82.09 

12.27 

82.03 

12.63 

83 

84 

83.18 

11.69 

i83.13 

12.05 

83.03 

12.42 

83.02 

12.78 

84 

85 

84. 17 

1.1.83 

184.12 

12.20 

84.0* 

12.56 

84.01 

12.93 

85 

86 

85.16 

11.97 

I 85 .11 

12.34 

!85.06 

12.71 

85.00 

13.08 

86 

87 

86.15 

12.11 

1 86.10 

12.48 

I 86.04 

12.86 

85.99 

13.23 

87 

88 

87.14 

12.25 

i87.09 

12.63 

187.03 

13.01 

86.93 

13.39 

88 

89 

88.13 

12.39 

; 88.08 

12.77 

188.02 

13.16 

87.96 

13.54 

89 

90 

89.12 

12.53 

|89.07 

12.91 

189.01 

13.30 

83.95 

| 13.69 

90 

31 

90.11 

12.66 

90.06 

; 13.06 

90.00 

13.45 

89.94 

1 13.84 

91 

92 

91.10 

12.80 

i91.05 

i 13.20 

90.99 

13.60 

i90.93 

14.00 

92 

93 

92.09 

12.94 

92.04 

| 13.34 

91.98 

13.75 

j 91.92 

14.15 

93 

94 

93.09 

13.08 

1 93.03 

i 13.49 

92.97 

13.89 

| 92 . 91 

14.30 

94 

95 

94.08 

13.22 

94.02 

13.63 

93,96 

| 14.04 

93.89 

14.45 

95 

96 

95.07 

1 13.36 

95.01 

i 13.78 

94.95 

14. 19 

! 94.88 

14.60 

96 

97 

96.06 i 18.50 

96.00 

13.92 

95.93 

14.34 

95.87 

14.76 

9/ 

98 

97.05 

i 13.64 

,96.99 

14.06 

96.92 

14.49 

96.86 

14.91 

98 

99 

98.04 

13.78 

97.98 

; 14.21 

97.91 

14.63 

97.85 

15.06 

99 

100 

99.03 

13.92 

98.97 

14.35 

93.90 

14.78 

98.84 

15.21 

100 

6 
r n 

/— 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

«.* 

o 

C 

a 

cc 

Q 

82 Deg. 
i 

8 If Deg. 

! 

8 U 

Deg. 

I 81* 

1 

Deg. 

C/3 

• 

o 
































































































20 


TRAVERSE TABLE 


Distance. 

9 Deg. 

9$ Deg. 

9| Deg. 

1 

9.f Deg 

1 _ 

C/3 

«-♦- 

P? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

p 

1 

0.99 

0.16 

0.99 

0.16 

0.99 

0.17 

0.99 

0.17 

i 

2 

1.98 

0.31 

1.97 

0.32 

1.97 

0.33 

1.97 

0.34 

2 

3 

2.96 

0.47 

2.96 

0.48 

2.96 

0.50 

2.96 

0.51 

3 

4 

3.95 

0.63 

3.95 

0.64 

3.95 

0.66 

3.94 

0.68 

4 

5 

4.94 

0.78 

4.93 

0.80 

4.93 

0.83 

4.93 

0.85 

5 

6 

5,93 

0.94 

5.92 

0.96 

5.92 

0.99 

5.91 

1.02 

n 

7 

! 6,91 

L.10 

0.91 

1.13 

6.90 

1.16 

6.90 

1.19 

7 

8 

7.90 

1.25 

7.90 

1.29 

7.89 

1.32 

7.88 

1.35 

8 

9 

8.39 

1.41 

8.88 

1.45 

8.88 

' .49 

8.87 

' 52 

9 

to 

9.83 

1.56 

9.87 

1.61 

9.86 

r* cr 

1 • 

cr . flu 

1.69 

10 

11 

10.86 

1 .72 

10.86 

1.77 

10.85 

1.82 

10.84 

1.86 

ii 

12 

11.85 

1.88 

11.84 

1.93 

11.84 

1.98 

11.83 

2.03 

12 

13 

12.84 

2.03 

12.83 

2.09 

12.82 

2.15 

12.81 

2.20 

13 

14 

13.83 

2.19 

13.82 

2.25 

13.81 

2.31 

13.80 

2 37 

14 

15 

14.82 

2.35 

14.80 

2.41 

14.79 

2.48 

14.78 

2.54 

15 

10 

15.80 

2.56 

15.79 

2.57 

15.78 

2.64 

15.77 

2.71 

16 

17 

16.79 

2.66 1 

16.78 

2.73 

16.77 

2.81 

16.75 

2.88 

17 

13 

17.78 

2.82 | 

17.77 

2.89 

17.75 

2.97 

17.74 

3.05 

18 

19 

18.77 

2.97! 

18.75 

3.05 

18.74 

3. 14 

18.73 

3.22 

19 

20 

19.75 

3.13 

19.74 

3.21 

19.73 

3.30 

19.71 

3.39 

20 

21 

20.74 

3.29 

20.73 

3.38 

20.71 

3.47 

20.70 

3.56 

21 

22 

21.73 

3.44 

21.71 

3.54 

21.70 

3.63 

21.68 

3.73 

22 

23 

22.72 

3.60 

22.70 

3.70 

22.68 

3.80 

22.67 

3.90 

23 

24 

23.70 

3.75 

23.69 

3.86 

23.67 

3.96 

23.65 

4.06 

24 

25 

24.69 

3.91 

24.67 

4.02 

24.66 

4.13 

24.64 

4.23 

25 

20 

25.68 

4.07 

25.66 

4.18 

25.64 

4.29 

25.62 

4.40 

26 

27 

26.07 

4.22 

26.65 

4.34 

26.63 

4.46 

26.61 

4.57 

27 

28 

27.66 

4.38 

27.64 

4.50 

27.62 

4.62 

27.60 

4.74 

28 

29 

28.64 

4.54 

28.62 

4.66 

28.60 

4.79 

28.58 

4.91 

29 

30 

29.63 

4.69 

29.61 

4.82 

29.59 

4.95 

29.57 

5.08 

30 

31 

30.62 

4.85 

30.60 

4.98 

30.57 

5.12 

30.55 

5.25 

31 

32 

31.61 

5.01 

31.58 

5.14 

31.56 

5.28 

31.54 

5.42 

32 

33 

32.59 

5.16 

32.57 

5.30 

32.55 

5.45 

32.52 

5.59 

33 

34 

33.58 

5.32 

33.56 

5.47 

33.53 

5.61 

33.51 

5.76 

34 

35 

34.57 

5.48 

34.54 

5.63 

34.52 

5.78 

34.49 

5.93 

35 

36 

35.56 

5.63 

35.53 

5.79 

35.51 

5.94 

35.48 

6.10 

36 

37 

36.54 

5.79 

36.52 

5.95 

36.49 

6.11 

36.47 

6.27 

37 

33 

37.53 

5.94 

37.51 

6.11 

37.48 

6.27 

37.45 

6.44 

38 

39 

38.52 

6.10 

38.49 

6.27 

38.47 

6.44 

38.44 

6.60 

39 

40 

39.51 

6.26 

39.48 

6.43 

39.45 

6.60 

39.42 

6.77 

40 

41 

40.50 

6.41 

40.47 

6.59 

40.44 

6.77 

40.41 

6.94 

41 

42 

41.48 

6.57 

41.45 

6.75 

41.42 

6.92 

41.39 

7.11 

42 

43 

42.47 

6.73 

42.44 

6.91 

42.41 

7.10 

42.38 

7.28 

43 

44 

43.46 

6.88 

43.43 

7.07 

43.40 

7.26 

43.36 

7,45 

44 

45 

44.45 

7.04 

44.41 

7.23 

44.38 

7.43 

44.35 

7.62 

45 

46 

45.43 

7.20 

45.40 

7.39 

45.37 

7.59 

45.34 

7.79 

46 

4 7 

46.42 

7.35 

46.39 

7.55 

46.36 

7.76 

46.32 

7.96 

47 

4ft 

47.41 

7.51 

47.38 

7.72 

47.34 

7.92 

47.31 

8.13 

18 

49 

48.40 

7.67 

48.36 

7.88 

48.33 

8.09 

48.29 

8.30 

49 

50 

49.38 

7.82 

49.35 

8.04 

49.32 

8.25 

49.28 

8.47 

50 

© 

c 

£ 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 ® 
w 

3 

eg 

m 

• H 

G 

81 Deg. 

80f Deg. 

80-| 

Deg. 

80^ Deg. 

05 

Y 

t£ 

• 

ft 






































































































TRAVERSE TABLE. 


21 


tJ 

r+ 

P 

9 Deg. 

i 

9^ Deg. 

94 

i 

Deg. 

9f Deg. 

►— • 

GC 

f— > 

D 

O 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| Dep. 

1^4 til. 

Dep. 

P 

O 

? 

51 

50.37 

| 7.98 

50.34 

8.20 

50.30 

8.42 

50.26 

8.64 

"51 

52 

!51.36 

! 8.13 

51.32 

8.36 

51.29 

8.58 

51.25 

8.81 

52 

53 

!52.35 

8.29 

52.31 

8.52 

152.27 

8.75 

52.23 

8.98 

9.14 

53 

54 

153.34 

8.45 

! 53,30 

8.68 

!53.26 

8.91 

53.22 

54 

55 

:54.32 

8.60 

54 28 

8.84 

|54.25 

9.08 

54.21 

9.31 

I 55 

56 

155.31 

' 8.76 

! 55.27 

9.00 

55.23 

9.24 

1 55.19 

9.48 

50 

57 

1 56.30 

8.92 

56.26 

9.16 

56.22 

9.41 

i 66.18 

9.65 

57 

58 

157.29 

9.07 

57.25 

9.32 

'57.20 

9.57 

! 57. 16 

9.82 

58 

59 

58.27 

9.23 

58.23 

9 48 

58.19 

9.74 

|58.15 

9.99 

53 

60 

59.26 

9.39 

59.22 

9 (14 

59.18 

| 9.90 

59.13 

10.16 

00 

01 

60.25 

9.54 

60.21 

9.81 

60.1,6 

!10.07 

00.12 

10.33 

61 

02 

61.24 

9.70 

61.19 

9.97 

61.15 

! 10.23 

63.10 

10.50 

62 

63 

62.22 

9.86 

62.18 

10.13 

62.14 

10.40 

62.09 

10.67 

63 

64 

63.21 

10.01 

63.17 

10.29 

63.12 

I 10.56 

03.08 

10.84 

64 

05 

64.20 

10.17 

64.15 

10.45 

64.11 

i 10.73 

64.00 

11.01 

65 

66 

65.19 

! 10.32 

65.14 

10.61 

65.09 

10.89 

65 . 05 

11.18 

60 

67 

66.18 

10.48 

66.13 

10.77 

66.08 

11.06 

66.03 

11.35 

67 

68 

67.16 

10.64 

67.12 

10.93 

67.07 

11.22 

67.02 

1 1 .52 

68 

69 

68.15 

10.79 

68.10 

11.09 

68.05 

11.39 

68.00 

11.69 

69 

70 

69.14 

10.95 

69.09 

11.25 

69.04 

11.55 

68.99 

11.85 

10 

71 

70.13 

11.11 

70.08 

11.41 

70.03 

11.72 

69.97 

12.02 

71 

72 

71.11 

11.26 

71 .06 

11.57 

71.01 

11.88 

70.96 

32.19 

72 

73 

72.10 

11.42 

72.05 

11.73 

72.00 

12.05 

71.95 

12.36 

73 

74 

73.09 

11.58 

73.04 

11.89 

72.99 

12.21 

72.93 

12.53 

74 

75 

74.08 

11.73 

74.02 

12.06 

73.97 

12.38 

73.92 

12.70 

75 

76 

75.06 

11.89 

75.01 

12.22 

74.96 

12.54 

74.90 

12.87 

76 

77 

76.05 

12.05 

76.00 

12.38 

75.94 

12.71 

75.89 

13.04 

77 

78 

77.04 

12.20 

76.99 

12.54 

76.93 

12.87 

76.87 

13.21 

78 

79 

78.03 

12.36 

77.97 

12.70 

77.92 

13.04 

77.86 

13.38 

79 

80 

79.02 

12.51 

78.96 

12.86 

78.90 

13.20 

i78.84 

13.55 

80 

81 

80.00 

12.67 

79.95 

13.02 

79.89 

13.37 

79.83 

13.72 

81 

82 

80.99 

12.83 

80.93 

13.18 

80.88 

13.53 

80.82 

13.89 

82 

S3 

81.98 

12.98 

81.92 

13.34 

81.86 

13.70 

81.80 

14.06 

83 

84 

82.97 

13.14 

82.91 

13.50 

82.85 

13.86 

82.79 

14.23 

84 

85 

83.95 

13.30 

83.89 

13.66 

83.83 

14.03 

83.77 

14.39 

85 

86 

84.94 

13.45 

84.88 

13.82 

84.82 

14.19 

84.76 

14.56 

86 

87 

85.93 

13.61 

85.87 

13.98 

85.81 

14.36 

85.74 

14.73 

87 

88 

86.92 

13.77 

86.86 

14.15 

86.79 

14.52 

86.73 

14.90 

S3 

89 

87.90 

13.92 

87.84 

14.31 

87.78 

14.69 

87.71 

15.07 

89 

90 

88.89 

14.08 

88.83 

14.47 

88.77 

14.85 

88.70 

15.24 

90 

91 

89.88 

14.24 

89.82 

14.63 

89.75 

15.02 

89.69 

15.41 

91 

92 

90.87 

14.39 

90.80 

14.79 

90.74 

15.18 

90 67 

15.58 

92 

93 

91.86 

14.55 

91.79 j 

14.95 

91.72 

15.35 

91.66 

15.75 

93 

94 

92.84 

14.70 

92.78 

15.11 

92.71 

15.51 

92.04 

15.92 

94 

95 1 

93.83 

14.86 

93.76 

15.27 

93.70 

15.68 

93.63 

16.09 

95 

96 

94 82 

15.02 

94.75 | 

15.43 

94.68 

15.84 

94.61 

16.26 

96 

97 | 

95.81 ! 

15.17 

95.74 ! 

15.59 

95.67 

16.01 

95.00 

16 43 

97 

98 

96.79 

15.33| 

96.73 j 

15.75 

96.66 

16.17 

86.58 

16. «0 

SB 

99 

97.78 j 

15.49 j 

97.71 

15.91 

97.64 

16.34 

97.57 

16.77 

99 

100 

98.77 I 

15.64 

98.70 

16.07 

98.63 

16.50 

98.56 

16.93 

100 

0 

O 

a 

n 

*■> 

in 

p 

Dep. 

Lat. j 

i 

Dep. 

Lat. 

Dep. 

Lai. 

Dep. 

Lat. 

6 

y 

C 

81 Deg. 

80:f Deg. 

304 Deg. 

1 

80| Deg. 

cd 

C L 

S 










































































































TRAVERSE TABLE. 


■22 


Distance. 

10 Deg. 

i 

10 } Deg. 

1 

10} Deg. 

lOf Deg. 

Distance.1 

Lat. 

- 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0 . 

98 

0.17 

0.98 

0.18 

0.98 

0,18 

0.98j 

0.19 

1 

2 

1 . 

97 

0.35 

1.97 

0.36 

1.97 

0.36 

1.98 1 

0,37 

2 

3 

o 

95 

0.52 

2.95 

0.53 

2.95 

0.55 

2.95 I 

0 56 

3 

4 

3. 

94 

0.69 

3.94 

0.71 

3.93 

0.73 

3.93 

0.75 

4 

5 

4. 

92 

0.87 

4.92 

0.89 

4.92 

0.91 

4.91 

0.93 

5 

6 

5. 

91 

1 .04 

5.90 

1.07 

5.90 

1.09 

5.89 

] . 12 

6 

? 

G . 

89 

1.22 

6.89 

1.25 

6.88 

1.28 

6.88 

1.31 

7 

8 

7 . 

88 

1.39 

7.87 

1.42 

7.87 

1.46 

7.86 

1.49 

6 

9 

8 . 

8 G 

1.56 

8.86 

1.60 

8.85 

1.64 

8.84) 

1.68 

9 

10 

9. 

85 

1.74 

9.84 

1.78 

9.83 

1.82 

9.82) 

1.87 

iO 

11 

10 . 

83 

1.91 

10.82 

1.96 

10.82 

2.00 

10.81 I 

2.05 

11 

12 

11 . 

82 

2.08 

11.81 

2.14 

11.89 

2.19 

11.79 I 

2.24 

12 

13 

12 . 

80 

2.26 

12.79 

2.31 

12.78 

2.37 

12.77 , 

2.42 

13 

14 

13. 

79 

2.43 

13.78 

2.49 ! 

13.77 

2.55 

13.75 

2.61 

14 

15 

14. 

77 

2.60 

14.76 

2.67 

14.75 

2.73 

14.74 

2.80 

15 

JG 

15. 

7G 

2.78 

15.74 

2.85 

15.73 

2.92 

15.72 

2.98 

16 

17 

1G. 

74 

2.95 

16.73 

3.03 

16.72 

3.10 

16.70 

3.17 

17 

18 

17. 

73 

3.13 

17.71 

3.20 

17.70 

3.28 

17.68 

3.36 

18 

19 

18. 

71 

3.30 

18.70 

3.38 | 

18.68 

3.46 

18.67 

3.54 

19 

20 

19. 

70 

3.47 

19 .68 

3.56 

19.67| 

3.64 

19.65 

3.73 

20 

21 

20 . 

G8 

3.65 

20.66 

3.74 1 

20.65 1 

3.83 

20.63 

3.92 

21 

22 

21 . 

67 

3.82 I 

21.65 

3.91 , 

21 .63 

4.01 

21.61 

4.10 

22 

23 

22 . 

65 

3.99 | 

22.63 

4.09 

22.61 

4.19 

22.60 

4.29 

23 

24 

23 

64 

4.17 

I 23.62 

4.27 

23.60 

4.37 

23. -VS 

4.48 

24 

25 

24. 

62 

4,34 

!24.60 

4.45 

24.58 

4.56 

24.56 

4.66 

25 

26 

25. 

61 

4.51 

125.59 

4.63 

25.56 

4.74 

25.54 

4.85 

26 

27 

26 

59 

4.69 

126.57 

4.80 

26.55 

4.92 

26.53 

5.04 

27 

28 

27. 

57 

4.86 

27.55 

4.93 

27.53 

5.10 

27.51 

5.22 

28 

29 

28. 

56 

5.04 

28.54 

5.16 

28.51 

5.28 

I 28.49 

5.41 

29 

30 

29. 

54 

5.21 

29.52 

5.34 

29.50 

5.47 

29.47 

5.60 

30 

31 

30. 

53 

5.38 

30.51 

5.52 

30.48 

5.65 

30.46 

5.78 

31 

32 

31. 

51 

5.56 

31.49 

5.69 

31.46 

5.83 

31.44 

5.97 

32 

33 

32. 

50 

5.73 

32.47 

5.87 

32.45 

6.01 

32.42 

6.16 

33 

34 

33 

48 

5.90 

33.46 

6.05 I 

33.43 

6.20 

33.40 

6.34 

34 

35 

34 

47 

6.08 

34.44 

6.23 

34.41 

6.38 

34.39 

6.53 

35 

36 

35 

45 

6.25 

35.43 

6.41 

| 35.40 

0.56 

35.37 

6 . 71 

36 

37 

3G 

44 

' 6.42 

36.41 

6.58 

1 36.33 

6 .74 

136.35 

6.90 

37 

38 

37 

.42 

6.60 

137.39 

6.76 

37.36 

6.92 

37.33 

7.09 

38 

39 

38 

.41 

6.77 

38.38 

6.94 

38.35 

7.11 

38.32 

7.27 

39 

40 

39 

.39 

6.95 

39.36 

7.12 

39.33 

7.29 

39.30 

7.46 

40 

41 

40 

.38 

1 7.12 

140.35 

7.30 

40.31 

7.47 

40.28 

7.05 

41 

42 

i 41 

.36 

7.29 

41 .33 

/ *4:7 

41.30 

7.65 

41.26 

7.83 

42 

43 

42 

. 35 

7.47 

| 42.31 

7.65 

42.28 

7.84 

42.25 

8.02 

43 

44 

43 

.33 

7.64 

1 43.30 

7.83 

43.26 

S .02 

43.23 

8.21 

44 

45 

j 44 

.32 

7.81 

! 44.28 

8.01 

44.25 

8.20 

44.21 

8.39 

45 

46 

45 

.30 

7.99 

i 45.27 

8.19 

45.23 

8.38 

45.19 

8,58 

■16 

47 

46 

.29 

8.16 

46.25 

8.36 

46.21 

8 .57 

46.18 

8.77 

47 

• 48 

47 

.27 

1 8.34 

47.23 

8.54 

47.20 

8.75 

47.16 

8.95 

48 

49 

48 

. 26 

8.51 

,48.22 

8.72 

48.18 

8 .93 

48.14 

9.14 

49 

50 

49 

.24 

8.68 

49.20 

8.90 

49.16 

9.11 

49.12 

9.33 

50* 

» 

as 

o 

c 

j Dep. 

{ Lat. 

Dep. 

L.t. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance.j 

rt 

—> 

2 

Q 

1 

80 Deg. 

79.f Deg. 

791 Dog. 

79} Deg. 














































































































TRAVERSE JAHLE. 


23 


Dista 

1 

10 

Deg. 

10} Deg. 

10| 

Deg. 

10,1 Deg. 

O 

c/T 

5 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L tit. 

Dep. 

3 

O 

o 

51 

50.23 

8.86 

50.19 

9.08 

50.15 

9.29 

50,10 

9.51 

61 

52 

51.21 

9.03 

51.17 

9.25 

51.13 

9.48 

51.09 

9 70 

52 

53 

52.19 

9.20 

52.15 

9.43 

52.11 

9.66 

52.07 

9.89 

53 

54 

53.18 

9.38 

53.14 

9.61 

53.10 

9.84 

53.05 

10.07 

54 

55 

54.16 

9.55 

54.12 

9.79 

54.08 

10.02 

54.03 

10.26 

55 

50 

55.15 

9.72 

55.11 

9.96 

55.06 

10.21 

55.02 

10.45 

56 

57 156.13 

9.90 

56.09 

10.14 

56.05 

10.39 

56.00 

10.63 

57 

58 

57.12 

10.07 

57.07 

10.32 

57.03 

10.57 

56.98 

10.82 

58 

59 

58.10 

10.25 

58.06 

10.50 

58.01 

10.75 

57.96 

11.00 

59 

09 

59.09 

10.42 

59.04 

10.68 

59.00 

10.93 

58.95 

11.19 

60 

01 

60.07 

1 0.59 

60.03 

10.85 

59.98 

11.12 

59.93 

11.38 

61 

6*2 

61.06 

10.77 

61.01 

11.03 

60.96 

11 .30 

60.91 

11,56 

62 

63 

62.04 

10.94 

61.99 

11.21 

61.95 

1) .48 

61.89 

11.75 

63 

64 

63.03 

11.11 

62.98 

11.39 

62.93 

11.66 

62.88 

11.94 

64 

05 

64.01 

11.29 

63.96 

11.57 

63.91 

11.85 

63.86 

12.12 

65 

66 

65.00 

11.46 

64.95 

11.74 

64.89 

12.03 

64.84 

12.31 

66 

67 

65.98 

11.63 

65.93 

11.92 

65.88 

12.21 

65.82 

12.50 

67 

68 

66.97 

11.81 

66.91 

12.10 

66.86 

12.39 

66.81 

12.68 

68 

69 

67.95 

11.98 

67.90 

12.28 

67.84 

12.57 

67.79 

12.87 

69 

70 

68.94 

12.16 

68.88 

12.46 

68.83 

12.76 

68.77 

13.06 

70 

71 

69.92 

12.33 

169.87 

12.63 

69.81 

12.94 

69.75 

13.24 

7J 

72 

70.91 

12.50 

70.85 

12.81 

70.79 

13.12 

70.74 

13.43 

72 

73 

71.89 

12.68 

I 71.83 

12.99 

71.78 

13.30 

71.72 

13.62 

73 

74 

72.88 

12.85 

72.82 

13.17 

72.76 

13.49 

72.70 

13.80 

74 

75 

73.86 

13.02 

173.80 

13.35 

73.74 

13.67 

73.68 

13.99 

75 

76 

74.85 

13.20 

174.79 

13.52 

74.73 

13.85 

74.67 

14.18 

76 

77 

75.83 

13.37 

75.77 

13.70 

75.71 

14.03 

75.65 

14.36 

77 

78 

76.82 

13.54 

76.76 

13.88 

76.69 

14.21 

76.63 

14.55 

78 

79 

77.80 

13.72 

77.74 

14.06 

77.68 

14.40 

77.61 

14.74 

79 

80 

78.78 

13.89 

78.72 

14.24 

78.66 

14.58 

78.60 

14.92 

80 

81 

79.77 

14.07 

79.71 

14.41 

79.64 

14.76 

79.58 

15.11 

81 

82 

80.75 

14.24 

80.69 

14.59 

80.63 

14.94 

80.56 

15.29 

82 

83 

81.74 

14.41 

SI.68 

14.77 

81.61 

15.13 

81.54 

15.48 

83 

84 

82.72 

14.59 

82.66 

14.95 

82.59 

15.31 

82.53 

15.67 

84 

85 

83.71 

14.76 

83.64 

15.13 

S3.58 

15.49 

83.51 

15.85 

85 

86 

84.69 

14.93 

84.63 

15.30 

84.56 

15.67 

84.49 

16.04 

88 

87 

85.68 

15.11 

85.61 

15.48 

85.54 

15.85 

85.47 

16.23 

87 

88 

86.66 

15.28 

86.60 

15.66 

86.53 

16.04 

86.46 

16.41 

88 

89 

87.65 

15.45 

87.58 

15.84 

87.51 

16.22 

87.44 

16.60 

89 

90 

88.63 

15.63 

88.56 

16.01 

88.49 

16.40 

88.42 

16.79 

90 

91 

89.62 

15.80 

89.55 

16.19 

89.48 

16.58 

89.40 

16.97 

91 

92 

90.60 

15.98 

90.53 

16.37 

90.46 

16.77 

90.39 

17.16 

92 

93 

91.59 

16.15 

91.52 

16.55 

91.44 

16.95 

91.37 

17.35 

33 

94 i92.57 

16.32 

92.50 

16.73 

92.43 

17.13 

92.35 

17.53 

94 

95 

93.56 

16.50 

93.48 

16.90 

93.41 

17.31 

93.33 

17.72 

95 

96 

94.54 

16.67 

94.47 

17.08 

94.39 

17.49 

94.32 

17.91 

96 

97 

95.53 

16.84 

95.45 

17.26 

95.38 

17.68 

95.30 

18.09 

97 

98 

96.51 

17.02 

i96.44 

17.44 

96.36 

17.86 

96.28 

18.28 

98 

99 

97.50 

17.19 

97.42 

17.62 

97.34 

18.04 

97.26 

18.47 

99 

100 

98.48 

17.36 

98.40 

17.79 

98.33 

18.22 

98.25 

18.65 

100 

QJ 

V 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

aJ 

o 

fl 

+2 

93 

**\ 

80 Deg. 

791 Deg. 

79^ 

i 

Deg. 

79} Deg. 

d 

4-> 

cc 8 

• •"-•4 

1 3 

I 


t 
























































































24 


TKAVEK.SE TABLE. 


Distance. 

11 Deg. 

11| Deg. 

1 

11 £ 

Deg. 

11J Deg. 

C 
►— • 

& 

r-+- 

P 

2 

O 

? 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 I 

0.98 

0.19 

0.98 

0.20 

0.98 

0.20 

0.98 

0.20 

i 

2 I 

1.96 

0.38 

1.96 

0.39 

1.96 

0.40 

1.98 

0.41 

2 

3 1 

2.94 

0.57 

2.94 

0.59 

2.94 

0.60 

2.94 

0.61 

3 

1 I 

3.93 

0.76 

3.92 

0.78 

3.92 

0.80 

3.92 

0.82 

4 . 

5 

4.91 

0.95 

4.90 

0.98 

4.90 

’1.00 

4.90 

1.02 

5 1 

6 1 

5.89 

1.14 1 

5.88 

1.17 

5.88 

1.20 

5.87 

1.22 

6 

7 

6.87 

1 .34 , 

6.87 

1.37 

6.86 

1.40 

6.85 

1.43 

7 

8 

7.85 

1.53 

7.85 

1.56 

j 7.84 

1.59 

7.83 

1.63 

8 

9 

8.83 

1.72 

8.83 

1.76 

8.82 

1.79 

' 8.81 

1.83 

9 

10 

9.82 

1.91 1 

9.81 

1.95 

9.80 

1.99 

9.79 J 

2.04 

10 

' 11 

10.80 

2.10 

10.79 

2.15 

10.78 

2.19 

10.77 

2.24 

11 

12 

11.78 

2.29 

11.77 

2.34 

11.76 

2.39 

11.75 

2.44 

12 

13 

12.76 

2.48 

12.75 

2.54 

12.74 

2 .59 

12.73 

2.65 

13 

14 

13.74 

2.67 

13.73 

2.73 

13.72 

2.79 

13.71 

2.85 

14 

15 

14.72 

2.86 

14.71 

2.93 

14.70 

2.99 

14.69 

3.00 

15 

16 

15.71 

3.05 

15.69 

3.12 

15.68 

3.19 

15.66 

3.26 

16 

17 

16.69 

3.24 

16.67 

3.32 

!16.66 

3.39 

16.64 

3.46 

17 

18 

17.67 

3.43 

17.65 

3.51 

17.64 

3.59 

17.62 

3.66 

18 

19 

18.65 

3.63 

18.63 

3.71 

18.62 

3.79 

18.60 

3.87 

19 

20 

19.63 

3.82 | 

19.62 

3..90 

19.60 

3.99 

19.58 

4.07 

20 

21 

20.61 

4.01 I 

20.60 

4.10 

20.58 

4.19 

20.56 

4.28 

21 

22 

21.60 

4.20 

21.58 

4.29 

21.56 

4.39 

21.54 

4.48 

22 

23 

22.58 

4.39 

22.56 

4.49 

22.54 

4.59 

22.52 

4.68 

23 

s>A 

** 

23.56 

4.J>3 

23.54 

4.68 

23.52 

4.78 ! 

23.50 

4.89 

24 

25 

24.54 

4.77 

24.52 

4.83 

24.50 

4.98 

24.48 

5.09 

25 

26 

25.52 

4.96 

25.50 

5.07 

25.43 

5.18 

25.46 

5.30 

26 

27 

26.50 

5.15 

26.48 

5.27 

26.46 

5.38 

20.43 

5.50 

27 

28 

27.49 

5.34 

27.46 

5.46 

27.44 

5.58 

27.41 

5.70 

28 

29 

28.47 

5.53 

28.44 

5.66 

28.42 

5.78 

28.39 

5.91 

29 

30 

29.45 

5.72 

29.42 

5.85 

29.40 

5.93 ! 

29.37 

6.11 

30 

31 

30.43 

5.92 

30.40 

6.05 

30.38 

6.18 

30.35 

6.31 

31 

32 

31.41 

6.11 

31.39 

6.24 

31 .38 

6.38 

31.33 

6.52 

32 

33 

32.39 

6 30 

32.37 

6.44 

32.34 

6.58 

32.31 

6.72 

33 

34 

33.38 

6.49 

33.35 

6.63 

33.32 

6.78 

33.29 

6.92 

31 

35 

34.36 

6.68 

34.33 

6.83 

34.30 

6 .93 

34.27 

7. 13 

35 

36 

35.34 

6.87 

35.31 

7.02 

35.28 

7. 18 

35.25 

7.33 

36 

37 

36.32 

7.06 

36.29 

7.22 

36.26 

7.33 

36.22 

7.53 

37 

38 

37.30 

7.25 

37.27 

7.41 

37.24 

7.58 

37.20 

7.74 

38 

39 

33.28 

7.44 

38.25 

7.61 

38.22 

7.78 

38.18 

7.94 

39 

40 

39.27 

7.63 

39.23 

7.80 

39.20 

7.97 

39.16 

8.15 

40 

41 

40.25 

7.82 

40.21 8.00 

40.18 

8.17 

40.14 

8.35 

‘41 

42 

41 23 

8.01 

41.19 

8.19 

41.16 

8.37 

41.12 

8 .55 

42 

43 

42.21 

8.20 

42.17 

8.39 

42.14 

8.57 

42.10 

8.76 

43 

44 

43.19 

8.40 

43.15 

8.58 

43.12 

8.77 

43.08 

8.96 

44 

45 

44.17 

‘ 8.59 

44.14 

8.78 

44.10 8.97 

44.06 

9.16 

45 

46 

45.15 

| 8.78 

45.12 

8.97 

45.08 

9.17 

45.04 

9.37 

16 

47 

46.14 

8.97 

j46.10 

9.17 

46.06 

9.37 

46.02 

9.57 

<7 

48 

47.12 

9.16 

47.08 

9.36 

47.04 

| 9.57 

46.99 

9.78 

48 

49 148.10 

1 9.35 

| 48.06 

9.50 

48.02 

9.77 

47.97 

9.9S 

49 

50 

49.08 

9.54 

49.04 

9,75 

;49.00 

9.97 

48.95 

10.18 

50 

<6 

o 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

o 

c 

*-> 

• —4 

1 ° 

79 Dog. 

7Hf De^f. 

'8+ 

Deg. 

1 

78.} Deg. 

r* 

' .i 

I a 









































































































TKAVKhSK TABLE. 


O 


2 

73* 

r-*- 

P 

11 

Deg. 

11^ Deg. 

Hi 

Deg. 

113 Deg 

1 

O 

75 

o 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

I-i cl t. 

Dep. 

1 

| Lat. 

! Dep. 

S" 1 

3 

a 

© 

51 

50.06 

9.73 

50.02 

j 9.95 

49.98 

10.17 

49.93 

10.39 

51 I 

i 52 

151.04 

9.92 

51.00 

|10.14 

50.96 

110.37 

j50.91 

10.59 

! 52 j 

53 

;52.03 

I 10.11 

V . 93 

10.34 

51.94 

10.57 

■ 51.89 

10.79 

53 | 

54 

j 53.01 

110.30 

52.96 

10.53 

52.92 

10.77 

|52.87 

11.00 

! 54] 

55 

53.99 

10.49 

53.94 

10.73 

53.90 

10.97 

53.85 

11.20 

1 55 1 

56 

154.97 

10.69 

| 54.92 

10.93 

64.88 

11.16 

54.83 

11.40 

561 

57 

j55.95 

10.88 

55.90 

11.12 

55.86 

11.36 

55.8 ] 

11.61 

57 

58 

156.93 

j 11.07 

56.89 

11.32 

56.84 

11.56 

56.78 

11.81 

58 

59 

!57.92 

11.26 

| 57.87 

11.51 

57.82 

11.76 

57.76 

12.01 

59 

SO 

58.90 

11.45 

j 58.85 

11.71 

58.80 

11.96 

58.74 

112.22 

CO 

dl 

|59.88 

11.64 

1 59.83 

i 11.90 

59.73 

12.16 

59.72 

Tl2.42 

| 61 

62 

1 60.86 

11.83 

60.81 

12.10 

60.76 

12.36 

60.70 

112.63 

| 62 

63 

!61.84 

12.02 

!61.79 

12.29 

61.74 

12.56 

61.68 

i12.83 

j 63 

64 

62.82 

12.21 

162.77 

12.49 

62.72 

j 12.76 

62.66 

I 13.03 

64 | 

65 

63.81 

;12.40 

163.75 

12.68 

! 63.70 

12.96 

63.64 

13.24 

i 65 ji 

66 

64.79 

12.59 

64.73 

12.88 

i 64.68 

j 13.16 

j 64.02 

13.44 

1 66 | 

' 67 

65.77 

12.78 

65.71 

13.07 

;! 65.66 

13.36 

65.60 

13.64 

j l>7 | 

63 

66 .75 

12.98 

66.69 

13.27 

! 66.63 

13.56 

68.58 

13.85 

68 

69 

67.73 

13. 17 

67.67 

13.46 

67.61 

13.76 

67.55 

114.05 

69 

70 

63.71 

13.36 

68.66 

13.66 

68 .59 

13.96 

168 .53 

14.25 

70 

71 

69.70 

13.55 

69.64 

13.85 

69.57 

14.16 

- 69.51 

14.40 

71 

72 

70.68 

13.74 

70.62 

14.05 

70.55 

14.35 

i 70.49 

i14.66 

72 

73 

71.66 

113.93 

71.60 

14.24 

171.53 

j M.55 

j 71.47 

J 14.87 

73 

1 74 

72.64 

j 14.12 

72.58 

14.44 

72.51 

14.75 

1 72.45 

!15.07 

74 

75 

73.62 

!14.31 

73.56 

14.63 

73.49 

14.95 

73.43 

15.27 

75 

I 7 6 

74.60 

14.50 

74.54 

14.8.3 

74.47 

15.15 

i74.41 

15.48 

76 

77 

75.59 

14.69 

75.52 

15.02 

75.45 

15.35 . 

75 39 

15.63 

77 

f 78 

76.57 

14.88 

76.50 

15.22 

76.43 

15.55 ; 

76.37 

15.88 

73 j 

I 79 

77.55 

15.07 

77.48 

15.41 

77.41 

15.75 j 

77.34 

16.09 

79 | 

SO 

78.53 

15.26 

78.46 

15.61 

78.39 

15.95 | 

78.32 

16.29 

so! 

81 

79.51 

15.46 

79.44 

15.80 

79.37 

16.15 I 

79.30 

16.49 

81 

82 

80.49 

15.65 

80.42 ; 

16.00 

80.35 

16.35 

80.28 

16.70 

82 

83 

81.48 

15.84 

81.41 | 

16.19 

81.33 

16.55 

81.26 

16.90 

83 

84 

82.46 

16.03 

82.39 

16.39 

82.31 

16.75 

82.24 

17.11 

84 i 

85 

83.44 

16.22 

83.37 

16.58 

83.29 i 

16.95 

83.22 

17.31 ' 

85 

86 

84.42 

16.41 

84.35 

16.78 

84.27 

17.15 ; 

84.20 

17.51 j 

86 

87 

85.40 

16.60 

85.33 

16.97 

85.25 

17.35 

85.18 ; 

17.72 1 

87 

88 

86.38 

16.79 

86.31 

17.17 | 

86.23 

17.54 

86.16 ; 

17.92 ! 

88 

89 

87.36 

16.98 

87.29 

17.36 

87.21 

17.74 j 

87.14 1 

18.12 | 

89 

90 

88 .35 

17.17 

88.27 

17.56 

88.19 

17.94 1 

88.11 j 

18.33 

90 

91 

89.33 

17.36 

89.25 

17.75 

89.17 . 

18.14 1 

89.09 

18.53 | 

91 

1 92 

90.31 ! 

17.55 

90.23 

17.95 

90.15 ! 

18.34 

90.07 

18.74 

92 

I 93 

91.29 ! 

17.75 

91.21 

18.14 | 

91.13 ! 

18.54 

91.05 

18.94 

93 

94 

92.27 

17.94 

92. 19 

18.34 j 

92.11 1 

18.74 

92.03 

19.14 , 

94 

l 95 ! 

93.25 

18. 13 

93.17 

18.53 | 

93.09 

18.94 

93.01 

19.35 

95 

1 96 

94.24 

18.32 

94.16 

18.73 

94.07 | 

19.14 

93.99 | 

19.55 

96 

97 I 

95.22 

18.51 

95.14 

18.92 

95.05 

19.34 

94.97 ; 

19.75 

97 

98 

96.20 

18.70 

96.12 

19.12 

96.03 

19.54 

95.95 

19.96 

98S 

99 

97.18 

18.89 

97.10 

19.31 

97.01 

19.74 

96.93 

20.16 

99 | 

! 00 

98.16 

19.08 

98.08 I 

19.51 

97.99 

19.94 

97.90 

20.36 

00 8 

a: 

c 

a 

Dep. 

Lat. 

Dep. ! 

Lat. 

Dep. I 

Lat. 

Dep. 

1 

Lat. 

1 

£ 

V 

« 

cd 

£ 

79 Deg. 

78.f Deg. 

78A Deg. 

I 

78 i Deg. * 

cd 

—> 

& j 
































































































































26 


TRAVERSE TARLE. 


Distance. 

12 Deg 

12} Deg. 

m 

Deg. 

12| Deg. 

o 

r—«• 

to 

<-► 

P 

Lett. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

cs 

• 

1 

0.98 

0.21 

0.98 

0.21 

0.98 

0.22 

0.93 

0.22 

1 

2 

1.96 

0.42 

1.95 

0.42 

1.95 

0.43 

1.95 

0.44 

2 

3 

2.93 

0.62 

2.93 

0.64 

2.93 

0.65 

2.93 

0.66 

3 

4 

3.91 

0.83 

3.91 

0.85 

3.91 

0.87 

3.90 

0.88 1 

4 

5 

4.89 

1.04 

4.89 

1.06 

4.88 

1.08 

4.88 

1.10 | 

5 

6 

5.87 

1.25 

5.86 

1.27 

5.86 

1.30 

5.85 

1 .32 

6 

7 

6.85 

1.46 

6.84 

1.49 

. 6.83 

1.52 

6.83 

1 54 

7 

8 

7.83 

1.66 

7.82 

1.70 

7.81 

1.73 

7.80 

1 .77 

8 

9 

8.80 

1.87 

8.80 

1.91 

8.79 I 

1.95 

8.78 

1.99 

9 

10 

9.78 

2.08 

9.77 

2.12 

9.76 

2.16 

9.75 

2.21 

10 

11 

10.76 

2.29 

10.75 

2.33 

10.74 

2.38 

10.73 

2.43 

11 

12 

11.74 

2.49 

11.73 

2.55 

11.72 

2.60 

11.70 

2.65 

12 

13 

12.72 

2.70 

12.70 

2.76 

12.69 

2.81 

12.68 

2.87 

13 

14 

13.69 

2.91 

13.68 

2.97 

13.67 

3.03 

13.65 

3.09 

14 

15 

14.67 

3.12 

14.66 

3.18 

14.64 

3.25 

14.63 

3.31 

15 

16 

15.65 

3.33 

15.64 

3.39 

15.62 

3.46 

15.61 

3.53 

16 

17 

16.63 

3.53 

16.61 

3.61 

16.60 

3.68 

16.58 

3.75 

17 

18 

17.61 

3.74 

17.59 

3.82 

17.57 

3.90 

17.56 

3.97 

18 

19 

18.58 

3.95 

18.57 

4.03 

18.55 

4.11 

18.53 

4. 19 

19 

20 

19.56 

4.16 

19.54 

4.24 

19.53 

4.33 

19.51 

4.41 

20 

21 

20.54 

4.37 

20.52 

4.46 

20.50 

4.55 

20.48 

4.63 

21 

22 

21.52 

4.57 

21.50 

4.67 

21.48 

4.76 

21.46 

4.86 

DO 

— 

23 

22.50 

4.78 

22.48 

4.88 

22.45 

4.98 

22.43 

5.08 

23 

24 

23.48 

4.99 

23.45 

5.09 

23.43 

5.19 

23.41 

5.30 

24 

25 

24.45 

5.20 

24.43 

5.30 

24.41 

5.41 

24.38 

5.52 

25 

26 

25.43 

5.41 

25.41 

5.52 

25.38 

5.63 

25.36 

5.74 

26 

27 

26.41 

5.61 

26.39 

5.73 

26.36 

5.84 

126.33 

5.96 

27 

28 

27.39 

5.82 

27.36 

5.94 

27.34 

6.06 | 

127.31 

0.18 

28 

29 

28.37 

6.03 

28.34 

6.15 

28.31 

6.28 I 

128.28 
29.26 

6.40 

29 

30 

2.9.34 

6.24 

29.32 

6.37 

i 

29.29 

6.49 

6.62 

30 

31 

30.32 

6.45 

30.29 

6.58 

30.27 

6.71 

30.24 

6.84 

31 

32 

31.30 

6.65 

31.27 

6.79 

31.24 

6.93 

31.21 

7.06 

32 

33 

32.28 

6.86 

32.25 

7.00 

32.22 

7.14 

32.19 

7.28 

33 

34 

33.26 

7.07 

33.23 

7.21 

33.19 

7.36 

33.16 

7.50 

34 

35 

34.24 

7.28 

34.20 

7.43 

34.17 

7.58 

34.14 

7.72 

35 

36 

35.21 

7.48 

35.18 

7.64 

35.15 

7.79 

135.11 

7.95 

36 

37 

36.19 

7.69 

36.16 

7.85 

36.12 

8.01 

36.09 

8.17 

37 

38 

37.17 

7.90 

37.13 

8.06 

37.10 

8.22 

i37.06 

8.39 

38 

39 

38.15 

8.11 

38.11 

8.27 

38.08 

8.44 

33.04 

8.61 

39 

40 

39.13 

8.32 

39.09 

8.49 

39.05 

8.66 

39.01 

8.83 

40 

41 

40.10 

8.52 

40.07 

8.70 

40.03 

8.87 

39.99 

9.05 

41 

42 

41.08 

8.73 

41.04 

8.91 

41.00 

9.09 

40.96 

9.27 

42 

43 

42.06 

8.94 

42.02 

9.12 

41.98 

9.31 

41.94 

9.49 

43 

44 

43.04 

9.15 

43.00 

9.34 

42.96 

9.52 

42.92 

9.71 

44 

45 

44.02 

9.36 

43.98 

9.55 

43.93 

9.74 

43.89 

9.93 

45 

46 

i44.99 

9.56 

44.95 

9.76 

44.91 

9.96 

44.87 

10.15 

46 

47 

45.97 

9.77 

45.93 

9.97 

45.89 

10.17 

45.84 

10.37 

47 

48 

46.95 

9.98 

46.91 

10.18 

46.86 

10.39 

46.82 

10.59 

48 

49 

47.93 

10.19 

47.88 

10.40 

47.84 

10.61 

47.79 

10.81 

i 49 

50 

48.91 

10.40 

48.86 

10.61 

48.81 

10.82 

|48.77 

11.03 

! 50 

a! 

8 

a 

Dep. 

| Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

! 

Dep. 

t* 

l"T 

1 § 

+-> 

CC 

5 

78 Deg 

773 Deg. 

i*r**r » 

! 

Deg. 

77} Deg. 

+-» 

to 

I s 

I 


j 









































































































traverse table. 


27 


o 
►— • 
CO 
«-*■ 
p 

12 

Deg. 

12| 

Deg. 

i 

12* 

Deg. 

12| Deg. 

D 

r 

* ■* 

o 

o 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

! Dep. 

Lat. 

D©p. 

1 ~ 

a 

51 

49.89 

10.60 

49.84 

10/82 

49.79 

|11.04 

49.74 

11.26 

51 

52 

50.86 

10.81 

1 50.82 

11.03 

(50.77 

11.25 

-50.72 

11.48 

| 52 

53 

51.84 

11.02 

1 51.79 

11.25 

51.74 

11 .47 

51.69 

1 11.70 

53 

54 

52.82 

11.23 

1 52.77 

11.46 

52.72 

11.69 

52.67 

11.92 

1 54 

55 

53.80 

11.44 

53.75 

11.67 

53.70 

11.90 

53.64 

12.14 

55 

56 

54.78 

11.64 

54.72 

11. 88 

!54.67 

12.12 

54.62 

12.36 

j 56 

57 

55.75 

11.85 

55.70 

12.09 

55.65 

12.34 

55.59 

12.58 

1 57 

58 

-56.73 

12.06 

56.68 

12.31 

56.63 

12.55 

56.57 

12.80 

i 58 

59 

57.71 

12.27 

1 57.66 

12.52 

57.60 

12.77 

|57.55 

13.02 

; 5a 

60 

5S. 69 

12.47 

| 58.63 

12.73 

I58.58 

j 12.99 

|58.52 

13.24 

60 

61 

59.67 

12.68 

59.61 

12.94 

j59.55 

113.20 

59.50 

13.46 

i 64 

62 

60,65 

12.89 

! 60.59 

13.16 

;60.53 

i13.42 

60.47 

13.68 

, 62 

63 

61.62 

13.10 

61.57 

13.37 

61.51 

I 13.64 

61.45 

13.90 

63 

64 

62.60 

13.31 

62.54 

13.58 

62.48 

j 13.85 

62.42 

14.12 

1 64 

65 

63.58 

13.51 

63.52 

13.79 

- 63.46 

14.07 

63.40 

14.35 

65 

66 

64.56 

13.72 

64.50 

14.00 

|64.44 

1 14.29 

64.37 

14.57 

fin 

67 

65.54 

13.93 

65.47 

14.22 

1 65.41 

14.50 

65.35 

14.79 

67 

68 

66.51 

14.14 

66.45 

14.43 

j 66.39 

14.72 

66.32 

15.01 

68 

69 

67.49 

14.35 

67.43 

14.64 

67.36 

14.93 

67.30 

15.23 

69 

70 

68.47 

14.55 

68.41 

14.85 

j68.34 

15.15 

68.27 

15.45 

70 

71 

69.45 

14.76 

69.38 

15.06 

69.32 

15.37 

69.25 

15.67 

71 

72 

70.43 

14.97 

70.36 

15.28 

70.29 

15.58 

70.22 

15.89 

72 

78 

71.40 

15.18 

1 71.34 

15.49 

|71.27 

15.80 

71.20 

16.11 

73 

74 

72.38 

15.39 

72.32 

15.70 

j 72.25 

16.02 

72.18 

16.33 

74 

75 

73.36 

15.59 

73.29 

15.91 

i73.22 

16.23 

73.15 

16.55 

75 

76 

74.34 

15.80 

74.27 

16.13 

174.20 

16.45 

74.13 

16.77 

76 

77 

75.32 

16.01 

75.25 

16.34 

'75.17 

16.67 

75.10 

16.99 

7 7 

78 

76.30 

16.22 

76.22 

16.55 

76.15 

16.88 

76.08 

J 7.21 

78 

79 

77.27 

16.43 

77 20 

16.76 

77.13 

17.10 

77.05 

17.44 

79 

80 

78.25 

16.63 

78.18 

16.97 

78.10 

17.32 

78.03 

17.66 

80 

81 

79.23 

16.84 

79.16 

17.19 

79.08 

17.53 

79.00 

17.88 

si 

82 

80.21 

17.05 

80.13 1 

17.40 

80.06 

17.75 

79.98 

18.10 

82 

83 

81.19 | 

17.26 

8 i. 11 ] 

17.61 

81.03 

17.96 

80.95 

18.32 

83 

84 

82.16 

17.46 

82.09 j 

17.82 

82.01 

18.18 

81.93 

18.54 

84 

85 

83.14 

17.67 

83.06 

IS 04 

82.99 

18.40 

82.90 

18.76 

85 

86 

84.12 

17.88 

84.04 1 

18.25 

83.96 

18.61 

83.88 

18.98 

86 

87 

85.10 

18.09 

85.02 

18.46 

84.94 | 

18.83 

84.85 

19.20 1 

87 

88 

86.08 

18.30 

86.00 

18.67 

85.91 j 

19.05 

85.83 

19.42 I 

88 

89 

87.06 

18.50 

86.97 

18.88 

86.89 

15.26 

86.81 

19.64 | 

89 

90 

88.03 

18.71 

87.95 

19.10 

87.871 

19.48 

87.78 

19.86 

90 

91 

89.01 

18.92 

88.93 

19.31 

88.84 

19.70 1 

86,76 

20.08 

91 

92 

89.99 

19.13 

89.91 

19.52 

89.82 

19.91 1 

89.73 

26.30 

92 

93 

90.97 

19.34 

90.88 

19.73 

90.80 

20.13 

90.71 

20.52 

93 

94 

91.95 

19.54 

91.86 I 

19.94 

91.77 

20.35 

91.68 

20.75 

94 

95 

92.92 

19.75 

92.84 

20.16 

92.75 

20.56 

92.66 

20.97 j 

95 

96 

93.90 

19.96 

93.81 

20.37 

93.72 

20.78 

93.63 

21.19, 

96 

97] 

94.88 

20. 17 

94.79 

20.58 

94.70 

20.99 

94 -61 

24.41 

97 

98 1 

95.86 

20.38 I 

95.77 

20.79 

95.68 ! 

21.21 

95.58 

21.63 

98 

99 

96.84 

20.58 | 

96.75 

21.01 

96.65 1 

21.43 

96.56 j 

21.85 

99 

100 97.81 

20.79 

97.72 

21.22 

97.63 j 

21.64 

97.53 

22.07 

100 

• 

Zj { 
O 

c 1 

Dcp. 

» 

L (it. 

Dep. 

Lat. 

Dep. { 

Lat. 

Dep. 

Lat. 

cJ 

O 

r* 

■A | 

5 I 

78 Deg. 

Deg 

II 

77* Deg. 

77* Deg. 

d 

• H 

Q 

_ t 























































































































28 


TRAVERSE TABLE. 


o 
►— • 

U1 

«-► 

13 Deg. 

134 Deg. 

13£ Deg. 

I3.f Deg. 

C 

• 

Cfi 

P 

3 1 
O 

2 1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

o 

p 

11 

0.97 

0.23 

0.97 

0.23 

0.97 

0.23 

0.97 

0.24 

1 

' 2 1 

1.95 

0.45 

1.95 

0.46 

1.95 

0.47 

1.94 

0.48 

2 

,1 

2 92 

0.67 

2.92 

0.69 

2.92 

0.70 

2.91 

0.71 

3 

4 

3,90 

0.90 

3.89 

0.92 

3.89 

0.93 

3.89 

0.95 

4 

5 ! 

4.87 

1.12 

4.87 

1.15 

4.86 

1.17 

4.86 

1.19 

5 

6 

5.85 | 

1.35 

5.84 

1.38 

5.83 

1.40 

5.83 

1.43 

6 

7 

6.82 

1.57 

6.81 

1.60 

6.81 

1.63 

6.80 

1.66 

7 

a 

7.80 

1.80 

7.79 

1.83 

7.78 

1.87 

7.77 

1.90 

8 

y 

8.77 

2.02 

8.76 

2.06 

8.75 

2.10 

8.74 

2.14 

9 

10 

9.74 

2.25 

9.73 

2.29 

9.72 

2.33 

9.71 

2.38 

10 

11 

0.72 : 

2.47 

10.71 

2.52 

10.70 

2.57 

10.68 

2.61 

11 

12 

11.69 

2.70 

11.68 

2.75 

11.67 

2.80 

11.66 

2.85 

12 

13 

.2.67 

2.92 

12.65 

2.98 

12.64 

3.03 

12.63 

3.09 

13 

14 

13.64 

3.1oi 

13.63 

3.21 

13.61 

3.27 

13.60 

3.33 

14 

15 

'.4.62 

3.37 

14.60 

3.44 

14.59 

3.50 

14.57 

3.57 

15 

16 

.5.59 ! 

3.60 

15.57 

3.67 

15.56 

3.74 

15.54 

3.80 

16 

17 

:6.57 ! 

3.82 

16.55 

3.SO 

16.53 

3.97 

16.51 

4.04 

17 

IS 

>7.54 j 

4.05 

17.52 

4.13 

17.50 

4.20 

17.48 

4.2S 

18 

10 

1.8.51 1 

4.27 

18.49 

4.35 

18.48 

4.44 1 

18.46 

4.52 

19 

20 

19.49 

4.50 

19.47 

4.58 

19.45 

4.67 

19.43 

4.75 | 

20 

"2l 

20.46 

4.72 

20.44 

4.81 

20.42 

4.90 

20.40 ; 

4.99 1 

21 

4\0 

21.44 

4.95 

21.41 

5.04 

21.39 

5.14 

21.37 

5.23 

22 

23 

22.41 

5.17 

22.39 

5.27 

22.36 

5.37 

22.34 

5.47 

23 

24 

23.38 

5.40 

■23.36 

5.50 

23.34 

5.60 

23.31 

5.70 

24 

25 

24.36 

5.62 

24.33 

5.73 

24.31 

5.84 | 

24.28 

5.94 

25 

26 

25.33 

5.85 

25.31 

5.96 

25.28 

6.07 

25.25 

6.18 

26 

27 

26.31 

6.07 

26.28 

6. IS 

26.25 

6.30 

26.23 

6.42 

27 

28 

27.28 

6.30 

27.25 

6.42 

27.23 

6.54 

27.20 

6.66 

28 

29 

28.26 

6.52 

28.23 

6.65 

28.20 

6.77 

28.17 

6.89 

29 

30 

29.23 

6.75 

29.20 

6.88 

29.17 

7.00 

29.14 

7.13 

30 

31 

30.21 

6.97 

30.17 

7.11 

30.14 

7.24 

30.11 

7.37 

31 

32 

31.18 

7.20 

31.15 

7.33 

31.12 

7.47 

31.08 

7.61 

32 

33 

32.15 

7.42 

32.12 

7.56 

32.09 

7.70 

32.05 

7.84 

33 

34 

33.13 

7.65 

33.09 

7.79 

33.06 

7.94 

33.03 

8.08 

34 

35 

34.10 

7.87 

34.07 

8.02 

34.03 

8.17 

34.00 

8.32 

35 

36 

35.08 

8.10 

35.04 

8.25 

35.01 

8.40 

34.97 

8.56 

36 

37 

36.05 

8.32 

36.02 

8.48 

35.98 

8.64 

35.94 

8.79 

37 

38 

37.03 

8.55 

36.99 

8.71 

36.95 

8.87 

36.91 

9.03 

| 38 

39 

38.00 

8.77 

37.96 

8.94 

37.92 

9.10 

37.88 

9.27 

39 

40 

38.97 

9.00 

38.94 

9.17 

38.89 

9.34 

38.85 

9.51 

40 

41 

39.95 

9.22 

39.91 

9.40 

39.87 

9.57 

39.83 

9.75 

41 

42 

40.92 

9.45 

40.88 

9.63 

40.84 

9.80 

| 40.80 

9.98 

42 

43 

41.90 

9 67 

41.86 

9.86 

41.81 

10.04 

41.77 

10.22 

43 

44 

42.87 

9.90 

42.83 

19.08 

■12.78 

1 10.27 

42.74 

|10.46 

44 

45 

43.85 

10.12 

43.80 

10.31 

13.76 

j 10.51 

43.71 

10.70 

45 

46 

44.82 

10.35 

44.78 

10.54 

44.73 

! JO.74 

44.68 

10.93 

40 

47 

45.80 

10.57 

45.75 

10.77 

45.70 

10.97 

45.65 

11.17 

47 

48 

46.77 

10.80 

46.72 

11.00 

46.67 

11.21 

46.62 

11.41 

48 

49 

47.74 

11.02 

47.70 

11.23 

47.65 

11.44 

47.60 

11.65 

49 

50 

48.72 

11.25 

48.67 

11.46 

48.62 

11.67 

4S.57 

11.88 

50 

• 

a 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

a 

a 

c 

ct 

+-> 

in 

• H 
/-N 

77 Deg. 

76f Deg. 

i 

76i 

Deg. 

76| 

Deg. 

2 

CO 

5 







































































































TRAVERSE T.VHLE. QQ 


r~'~- 

C 

C/i 

r-*- 

P 

13 Deg 

13£ Deg. 

13* 

it 

Deg. 

i 

131 

Deg. 

n 

C-* 

i— 1 

c 

c 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

p 

3 

O 

CD 

.'31 

49.69 

11.47 

49 

.64 

11.69 

49.59 

11.91 

49.54 

3 2.12 

57 

52 

50.6 7 

1 11.70 

50 

.62 

11.92 

50.56 

12.14 

50.51 

12.36 

52 

53 

51 } 

51 .64 

{ 11.92 

51 

.50 

12.15 

51.54 

12.37 

51.48 

12.60 

54 

52.62 

12.15 

52 

. 56 

12.38 

52.51 

12.61 

52.45 

12.84 

64 

55 

63 . 59 

! 12.37 

! 53 

.54 

12.61 

53.48 

12.84 

! 53.42 

13.07 

55 

56 

• 54.56 

12.60 

54 

.51 

12.84 

54.45 

13.07 

54.40 

13.31 

56 

57 

i 55.54 

12.82 

55 

.48 

13.06 

55.43 

13.31 

55.37 

13.55 

57 

58 

56.5 1 

13.05 

56 

.46 

13.29 

56.40 

13.54 

56.34 

13.79 

58 

59 

57 .49 

j 13.27 

57 

.43 

13.52 

57.37 

13.77 

57.31 

14.02 

59 

60 

58.46 

! 13.50 

58 

.40 

13.75 

58.34 

14.01 

58.28 

14.26 

60 

Gl 

59.44 

13.72 

59 

.38 

13.98 

59.31 

14.24 

59.25 

14.50 

61 

G2 

60.41 

13.95 

GO 

.35 

14.21 

00.29 

14.47 

60.22 

14.74 

62 

63 

61.39 

14.17 

61 

.32 

14.44 

61.26 

14.71 

61.19 

14.97 

63 

64 

62.36 

14.40 

62 

.30 

14.67 

62.23 

14.94 

62.17 

15.21 

64 

65 

63.53 

14.62 

G3 

.27 

14.90 

63.20 

15.17 

63.14 

15.45 

65 

66 

64.3 5 

14.85 

64 

.24 

15.13 

64.18 

15.41 

64.11 

15.69 

66 

G7 

65.28 

15.07 

65 

.22 

15.36 

i65.15 

15.64 

65.08 

15.93 

67 

68 

66.26 

15.30 

66 

.19 

15.59 

66.12 

15.87 

66.05 

16.16 

68 

G9 

67.23 

15.52 

67 

.10 

15.81 

167.09 

16.11 

67.02 

16.40 

69 

70 

63.21 

15.75 

68 

.14 

16.04 

|68.07 

16.34 

67.99 

16.64 

70 

71 

69.18 

15.97 

69 

.11 

16.27 

i69.04 

16.57 

68.97 

16.88 

71 

72 

70.15 

16.20 

70 

.03 

16.50 

70.01 

16.81 

!69.94 

17.11 

72 

7 3 

71.13 

16.42 

71 

.06 

16.73 

70.98 

17.04 

70.91 

17.35 

73 

74 

72.10 

16.65 

72 

.03 

16.96 

71.96 

17.28 

71.88 

17.59 

74 

75 

73.08 

16.87 

73 

.00 

17.19 

72.93 

17.50 

72.85 

17.83 , 

75 

76 

74.05 

17.10 

73 

.98 

17.42 

73.90 

17.74 

73.82 

3 8.06 

76 

77 

75.03 

17.32 

74 

.95 

17.65 

74.87 

17.98 

74.79 

18.30 ! 

77 

78 

76.00 

17.55 

75 

92 

17.88 

75.84 

38.21 

75.76 

18.54 ! 

78 

79 

76.98 

17.77 

76 

90 

18.11 

76.82 

18.44 

76.74 

18.78 i 

79 

SO 

77.95 

18.00 

77 

87 

18.34 

77.79 

18.68 

77.71 

19.01 | 

80 

81 

78,92 

18.22 

78. 

84 

18.57 ; 

78.76 

18.91 

78.68 

19.25 ! 

81 

82 

79. GO 

18.45 

79. 

82 

18.79 

79.73 

3 9. 14 

79.65 

19.49 

82 

83 j 

80.87 

18.67 

80. 

79 

19.02 

80.71 

19.38 

80.62 

19.73 

83 

84 j 

81.85 

13.90 

81. 

76 

19.25 1 

81.68 

3 9.01 

81.59 

19.97 | 

84 

85 

82.82 

19.12 

82. 

74 

19.48 i 

82.65 

19.84 

82.56 

20.20 i 

85 

86 I 

83‘. 80 

19.35 

83. 

71 

19.71 

83.62 

20 • 08 

83.54 

20.44 1 

86 

87 ! 

84.77 I 

19.57 

84. 

68 

19.94 

84.60 ! 

20.31 

84.51 

20.68 

87 

88 

85.74 

19.80 

85. 

66 

20.17 1 

85.57 j 

20.54 

85.48 

20.92 

88 

89 | 

86.72 

20.02 

86. 

63 

20.40 | 

86.541 

20.78 

86.45 

21.15 

89 

90 ; 

S7.69 

20.25 

87. 

60 

20.63 

87.51| 

21.01 

87.42 

21.39 

90 

91 j 

88.67 

20.47j 

88. 

58 

20.8G 

88.49 

21.24 

88.39 

21.63 

91 

92 

89.64 

20.70 1 

89. 

55 

21.09 

89.46 

21.48 | 

89.36 

21.87 

92 

93 i 

90.62 

20.92 

90. 

52 j 

2» 32 ij 

90.43 

21.71 

90.33 

22.10 

93 

94 191.59 

21.15 

91. 

50 

21.54 

91.40 

21.94 

91.31 

22.31 

94 

95 

92.57 

21.37 

92. 

47 

21.77 j 

92.38 1 

22.18 

92.28 

22.58 

95 

96 

93.54 1 

21.60 

93. 

44 

22.00 

93.35 ! 

22.43 

93.25 

22.82 

96 

97 

94.51 

21.82 

94. 

42 

22.23 

94.32 

22.64 j 

94.22 

23.06 

97 

93 

95.49 | 

22.05 

95. 

39 

22.46 

95.29 

22.88 : 

95.19 

23.29 ; 

98 

99 

96.46 ; 

22.27 

96. 

36 

22.69 

96.26 

23.11 

96.16 

23.53 I 

99 

100 1 

97.44 

22.50 

97. 

34 1 

22.92 

97.24 

23.34 

97.13 

23.77 1 

100 

© 

V 

Deo. 

Lat. 

Dep. j 

Lat. 

Dep. 

Lat. | 

Dep. 

Lat. 

6 

o 

ri 

w 

Q 

77 Dew. 

13 

I 

76f Deg. | 

76| Deg. 

76i Deg. 

■n 

r/> 

Q 


/ 


21 






















































































































30 


TEAVERSE TABLE 


I 




1 

a 
►— • 

c n 

14 Deg. 

14} Deg. 

14| Deg. 

14} Deg. 

Distance.' 

3 

a 

? j 

Lat. ! 

Dep. 

IjcLt* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 1 

0.97 

0.24 

0.97 

0.25 

0.97 

0.25 

0.97 

0.25 

1 

2J 

1.94 

0.48 

1.94 i 

0.49 

1.94 

0.50 

1.93 

0.51 

2 

3 1 

2.91 

0.73 ! 

2.91 1 

0.74 

2.90 

0,75 

2.90 

0.76 

3 

4 

3.88 i 

0.97 

3.88 ! 

0.98 

3.87 

1.00 

3.87 

1.02 

4 

5 | 

4.35 

1.21 

4.85 

1.23 

4.84 

1.25 

4.84 

1.27 

5 

6 ! 

5.82 

1.45 

5.82 

1.48 

5.81 

1.50 

5.80 

1.53 

6 

7 

6.79 

I . 69 

6.78 

1 ■ 72 | 

6.78 

1 .75 | 

6.77 

1.78 ' 

7 

8 , 

7.76 

1.94 

7.75 

1.97 j 

7.75 ■ 

2.00 

7.74 

2.04 

8 

9 

8.73 

2.18 

8.72 | 

2.22 

8.71 j 

2.25 ! 

8.70 

2.29 

9 

10 

9.70 

2.42 

9.69 

2.46 ] 

9.68 

2.50 ; 

9.67 

2.55 

:o 

71^ 

10.67 

2.66 

10.66 ! 

2.71 

10.65 

2 . 75 

10.64 1 

2.80 

i i 

12 

11.64 

2.90 i 

11.63 1 

2.95 

11.62 

3.00 ! 

11.60 

3.06 

12 

13 

12.61 

3.15 

12.60 

3.20 

12.59 

3.25 | 

12.57 

3.31 

13 

14 

13.58 

3.39 

13.57 

3.45 1 

13.55 

3.51 

13.54 

3.56 

14 

15 

14.55 

3.63 

14.54 

3.69 

14.52 

3.76 

14.51 

3.82 

15 

16 

15.52 

3.87 

15.51 

3.94 1 

15.49 

4.01 

15.47 ; 

4.07 

16 

17 

16.50 

4.11 

16.43 

4.18 

16.46 

4.26 

16.44 1 

4.33 

17 

18 

17.47 

4.35 

17.45 

4.43 

17.43 

4.51 

17.41 I 

4.58 

18 

19 

18.44 

4.60 

18.42 

4.68 

18.39 i 

4.76 

18.37 

4.84 

19 

20 

19.41 

4.84 

19.38 

4.92 

19.36 

5.01 

19.34 

5.09 

20 

21 

20.38 

5.08 

20.35 

5.17 

20.33 

5.26 

20.31 

5.35 

21 

22 

21.35 

5.32 

21.32 

5.42 

21.30 

5.51 

21.28 

5.60 

22 

23 

22.32 

5.56 

22.29 

5.66 

22.27 

5.76 

22.24 

5.86 

23 

24 

23.99 

5.81 

l23.26 

5.91 

23.24 

6.01 

23.21 

6 . L1 

24 

25 

24,26 

6.05 

24.23 

6.15 

24.20 

6.26 

24.18 

6.37 

25 

26 

25.23 

6.29 

25.20 

6.40 

25.17 

6.51 

25.14 

6.62 

26 

27 

26.20 

6.53 

26.17 

6.65 

26.14 

6 . 76 ; 

26.11 

6.87 

27 

23 

27.17 

6.77 

27.14 

6.89 

27.11 

7.01 

27.08 

7.13 

28 

29 

28.14 

7.02 

2S.11 

7.14 

28.08 

7.26 

28.04 

7.33 

29 

30 

29.11 

7.26 

29.08 

7.38 

29.04 

| 7.51 

29.01 

7.64 

30 

31 

30.08 

7.50 

30.05 

7.63 

30.01 

7.76 

29.98 

7.89 

31 

32 

31.05 

7.74 

31.02 

7.88 

30.98 

8.01 

30.95 

8.15 

32 

33 

32.02 

7.93 

31.98 

8.12 

31.95 

8.26 

31.91 

8.40 

33 

34 

32.99 

8.23 

32.95 

8.37 

32.92 

8.51 

32.88 

8.66 

34 

35 

33.96 

8.47 

33.92 

8.62 

33.89 

8.70 

33.85 

i 8.91 

35 

36 

34.93 

8.71 

34.89 

8.86 

34.85 

9.01 

34.81 

! 9.17 

36 

37 

35.90 

8.95 

35.86 

9.11 

35.82 

9.26 

35.78 

i 9.42 

37 

33 

36.87 

9.19 

36.83 

9.35 

36.79 

9.51 

36.75 

9.67 

38 

39 

37.84 

9.44 

37.80 

9.60 

37.76 

9.76 

37.71 

1 9.93 

39 

40 

38.81 

9 . 63 

38.77 

9.85 

38.73 

10.02 

38.68 

10.18 

40 

41 

39.78 

9.92 

39.74 

10.09 

39.69 

10.27 

39.65 

| 10.44 

41 

42 

40.75 

10.16 

40.71 

10.34 

40.66 

10.52 

40.62 

10.69 

42 

43 

41.72 

10.40 

41.68 

10.58 

41.63 

10.77 

41.58 

10.95 

43 

44 

42.69 10.64 

42.65 

10.83 

42.60 

11.02 

42.55 

11.20 

44 

45 

143.66 

10.89 

43.62 

11.08 

43.57 

11.27 

43.52 

1 11.46 

45 

46 

44.63 

11.13 

44.58 

11.32 

44.53 

11.52 

44.48 

11.71 

46 

47 

45.60 

11.37 

45.55 

11.57 

45.50 

11.77 

45.45 

111.9? 

47 

48 

46.57 

11.61 

46.52 

11.82 

46.47 

12.02 

46.42 

12.22 

48 

49 

47.54 

11.85 

47.49 

12.06 

47.44 

12.27 

47.39 

12 .48 

49 

50 

,48.51 

j 12.10 

48.46 

|12.31 

43.41 

12.52 

48.35 

12 73 

50 

Distance, 

Dep. 

j Lat. 

; Dep. 

i 

j Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

a! 

o 

G 

ei 

73 

5 

76 Deg. 

75} Deg. 

751 Deg. 

75i Deg. 

i 
































































































































TRAVERSE TABLE 


O 1 


G 
►—» 
CD 
(4 

P 

14 Deg. 

14^ Deg. 

14i 

Deg. 

14f Deg. 

I - 

i_ 

3 

n 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 o 
? 

61 

49.49 

!12.34 

49.43 

12.55 

49.38 

12.77 

49.32 

12.98 

51 

52 

50.46 

12.58 

50.40 

12.80 

50.34 

13.02 

50.29 

13.24 

52 

53 

51.43 

12.82 

51.37 

13.05 

51.31 

13.27 

51.25 

13.49 

53 

54 

52.40 

13.06 

52.34 

13.29 

52.28 

13.52 

52.22 

13.75 

54 

55 

53.37 

13.31 

53.31 

13.54 

53.25 

13.77 

53.19 

14.00 

55 

56 

54.34 

13.55 

54.28 

13.78 

54.22 

14.02 

54.15 

14.26 

50 

57 

55.31 

13.79 

55.25 

14.03 

55.18 

14.27 

55.12 

14.51 

57 

59 

56.28 

14.03 

56.22 

14.28 

56.15 

14.52 

56.09 

14.77 

! 58 

59 

57.25 

14.27 

57.18 

14.52 

57.12 

14.77 

57.06 

15.02 

59 

60 

58.22 

14.52 

58.15 

14.77 

58.09 

15.02 

58.02 

15.28 

60 

61 

59.19 

14.76 

59.12 

15.02 

59.06 

15.27 

58.99 

I 15.53 

6 i; 

62 

60. 16 

15.00 

60.09 

15.26 

60.03 

15.52 

59.96 

15.79 

62 

63 

61.13 

15.24 

61.06 

15.51 

60.99 

15.77 

1 60.92 

16.04 

63 

64 

62.10 

15.48 

62.03 

15.75 

61.96 

16.02 

j 61.89 

16.29 

64 

65 

63.07 

15.72 

63.00 

16.00 

62.93 

16.27 

| 62.86 

16.55 

65 

66 

64.04 

15.97 

63.97 

16.25 

63.90 

16.53 

| 63.S3 

16.80 

66 

67 

65.01 

16.21 

64.94 

16.49 

64.87 

16.78 

64.79 

17.06 

67 

68 

65.98 

16.45 

65.91 

16.74 

65.83 

17.03 

65.76 

17.31 

68 

69 

66.95 

16.09 

66.88 

16.98 

66.80 

17.28 

66.73 

17.57 

69 

70 

67.92 

16.93 

67.85 

17.23 

67.77 

17.53 

67.69 

17.82 

70 

71 

68.89 

17.18 

68.82 

17.48 

68 .74 

17.78 

68.66 

18.08 

71 

72 

69.86 

17.42 

69.78 

17.72 

69.71 

18.03 

69.63 

18.33 

72 

73 

70.83 

17.66 

70.75 

17.97 

70.67 

18.28 

70.59 

18.59 

73 

74 

71.80 

17.90 

71.72 

18.22 

71.64 

18.53 ! 

71.56 

18.84 

74 

75 

72 77 

18.14 

72.69 

18.46 

72.61 

18.78 j 

72.53 

19.10 

75 

76 

73.74 

18.39 

73.66 

18.71 

73.58 

19.03 

73.50 

19.35 

76 

77 

74.71 

18.63 

74.63 

18.95 

74.55 

19.28 

74.46 

19.60 

77 

78 

75.68 

18.87 

75.60 

19.20 

75.52 

19.53 

75.43 

19.80 

78 

79 

76.65 

19.11 

76.57 

19.45 

76.48 

19.78 

76.40 

20.11 

79 

80 

77.62 

19.35 

77.54 

19.69 

77.45 

20.03 

77.36 

20.37 

80 

81 

78.59 

19.60 

78.51 

19.94 

78.42 

20.28 

78.33 

20.62 

81 

82 

79.56 

19.84 

79.48 

20.18 

79.39 

20.53 

79.30 

20.88 

82 

83 

80.53 

20.08 

80.45 

20.43 

80.36 

20.78 

80.26 

21.13 

83 

84 

81.50 

20.32 

81.42 

20.68 

81.32 

21.03 

81 .23 

21.39 

84 

85 

82.48 

20.56 

82.38 

20.92 

82.29 

21,28 

82.20 

21.64 

85 

86 

83.45 

20.81 

83.35 

21.17 

83.26 

21.53 

S3.17 

21.90 

86 

87 

84.42 

21.05 

84.32 

21.42 

84.23 

21.78 

84.13 

22.15 

87 

88 

85.39 

21.29 

85.29 

21.66 

85.20 

22.03 

85.10 

22.41 

88 

89 

86.36 

21.53 

86.26 

21.91 

86.17 

22.28 

86.07 

22.66 

89 

90 

87.33 

21.77 

87.23 

22.15 

87.13 

22.53 

87.03 

22.91 

90 

91 

88.30 

22.01 

88.20 

22.40 

88.10 

22.78 

88.00 

23.17 

91 

92 

89.27 

22.26 

89.17 

22.65 

89.07 

23.04 

88.97 

23.42 

92 

93 

90.24 

22.50 

90.14 

22.89 

90.04 

23.29 

89.94 

23.68 

93 

94 

91.21 

22.74 

91.11 

23.14 

91.01 

23.54 I 

90.90 

23.93 

94 

95 

92.18 

22.98 

92.08 

23.38 

91.97 

23.79 

91.87 

24.19 

95 

96 

93.15 

23.22 

93.05 

23.63 

92.94 j 

24.04 

92.84 

24.44 

96 

97 

94.12 

23.47 

94.02 

23.88 

93.91 

24.29 

93.80 

24.70 

97 

98 

95.09 

23.71 

94.98 

24.12 

94.88 

24.54 

94.77 

24.95 

98 j 

99 

96.06 

23 95 

95.95 

24.37 

95.85 

24.79 

95.74 

25.21 

99 I 

100 

97.03 

24-19 

96.92 

24.62 

96.81 

25.04 

96.70 

25.46 

100 

oS 

g 

Dep. 

Lat. 

| 

Dep. ! 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

cs> \ 

V g 

c 3 

ci 

• -H 

~ 1 

76 Deg. 

75| Deg 

7 51 Deg. 

75i Deg 

cd g 
■*—< 1 

J 












































































































TRAVERSK TAHLE. 


| Distance. 
L —_ 

15 Deg. 

15i Deg. 

15£ 

Deg. 

153 Deg. 

P. 

73 

P 

Lat. j 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

CO 

*" T 

0.97 

0.26 

0.96 

0.26 

0.96 

0.27 

0.96 

0,27 

T 

2 

1.93 

0.52 

1.93 

0.53 

1 .93 

0.53 

1.92 

0 .54 

2 

3 

2.90 

0.78 

2.39 

0.79 

2.89 

0.80 

2.89 

0.81 

3 

4 

3.86 

1.04 

3.86 

1.05 

3.85 

1.07 

3.85 

1.09 

4 

r> 

4.83 

1.29 

4.82 

1.32 

4.82 

1 .34 

4.81 

1.36 

5 

! 6 

5.80 

1.55 

5.79 

1.58 

5.78 

1.60 | 

5.77 

1.63 

6 

7 

G. 76 

1.81 

6.75 

1.84 

6.75 

1.87 

6.74 

1.90 

7 

8 '! 

7.73 

2.07 

7.72 

2.10 

7.71 

2.14 | 

7.70 

2.17 

' 8 

9 

8.69 , 

2.33 

8.63 

2.37 1 

8.67 

2.41 

8.66 

2.44 

9 

10 

9.66 

2.59 

9.65 

2.63 j 

9.64 

2.67 

9.62 

2.71 

10 

11 

10.63 

2.85 1 

10.61 

2.89 

10.60 

2.94 ; 

10.59 

2.99 

11 

12 

11.59 

3.11 1 

11.58 

3.16 

11.56 

3.21 

11.55 

3.26 

12 

13 

12.56 

3.36 

12.54 

3.42 

12.53 

3.47 i 

12.51 

3.53 

13 

14 

13.52 

3.62 

13.51 

3.68 i 

13.49 

3.74 I 

13.47 

3.80 

14 

15 

14.49 

3.88 

14.47 

3.95 

14.45 

4.01 

14.44 

4.07 

15 

16 

15.45 

4.14 

15.44 

4.21 

15.42 

4.28 

15.40 

4.34 

16 

17 

16.42 

4.40 

16.40 

4.47 

16.33 

4.54 

16.36 

4.61 

17 

IS 

17.39 

4.66 

17.37 

4.73 

17.35 

4.81 1 

17.32 

4.89 

18 

19 

18.35 

4.92 

18.33 

5.00 

18.31 

5.08 

18.29 

5.16 

19 

20 

19.32 

5.18 

19.30 

5.26 

19.27 

5.34 J 

19.25 

5.43 

20 

21 

20.23 

5.44 

20.26 

5.52 * 

20,24 

5.61 

20.21 

5.70 

21 

22 

21.25 

5.69 

21.23 

5.79 1 

21.20 

5.88 

21.17 

5.97 

99 

23 

22.22 

5.95 

22.19 

6.05 j 

22.16 

6.15 

22.14 

6.24 

23 

24 

23. 18 

6.21 

23.15 

G.31 

23.13 

6.41 

23.10 

6.51 

24 

25 

24.15 

6.47 

24.12 

6.58 

6.84 

24.09 

6.63 

24.06 

6.79 

25 

26 

25.11 

6.73 

25.03 

25.05 

6 .95 

25.02 

7.06 

26 

27 

26.08 

6.99 

26.05 

7.10 

26.02 

7.22 

25.99 

7.33 

27 

28 

27.05 

7.25 

27.01 

7.36 

26.98 

7.48 

26.95 

7.60 

28 

29 

28.01 

7.51 

27.98 

7.63 

27.95 

7.75 | 

27.91 

7.87 

29 

30 

28.98 

7.76 

,28.94 

7.89 

28.91 

8.02 

28.87 

8.14 

30 

31 

29.94 

8.02 

29.91 

8.15 

29.87 

8.28 

29.84 

8.41 

31 

32 

30.91 

8.28 

30.87 

8.42 

30.84 

8.55 

30.80 

8.69 

32 

33 

31.83 

8 .54 

31.84 

8.68 

31.80 

8.82 i 

31.76 

8.96 

33 

34 

32.84 

8.80 

32.80 

8.94 : 

32.76 

9.09 | 

32.72 

9.23 

34 

35 

33.81 

9.06 

33.77 

9.21 ! 

33.73 

9.35 

33.69 

9.50 

35 

36 

34.77 

9.32 

34.73 

9.47 

34.69 

9.62 

34.65 

9.77 

36 

37 

35.74 

9.58 

35.70 

9.73 ! 

35.65 

9.89 

35.61 

10.04 

37 

38 

36.71 

9.84 

36.66 

10.00 ! 

36.62 

10.16 

36.57 

| 10.31 

38 

39 

37.67 

10.09 

37.63 

10.26 

37.58 

10.42 

37.54 

10.59 

39 

40 

38.64 

10.35 

38.59 

10.52 

38.55 

10.69 

39.50 

10.86 

40 

41 

39.60 

10.61 

39.56 

, 10.78 

39.51 

10.96 

1 39.40 

11.13 

41 

42 

40.57 

10.87 

40.52 

11.05 

40.47 

11.22 

j 40.42 

11.40 

42 

43 

41.53 

,11.13 

41.49 

! 11.31 

41.44 

11.49 

41.39 

11.67 

43 

44 

42.50 

11.39 

1 42.45 

; 11.57 

42.40 

11.76 

! 42.35 
! 43.31 

ill.94 

44 

45 

43.47 

11.65 

43.42 

11.84 

43.36 

12.03 

12.21 

45 

46 

1 44.43 

11.91 

I 44.38 

12.10 

44.33 

12.29 

44.27 

1 2 .49 

46 

47 

; 45.40 

12.16 

1 45.35 

12 .3G 

45.29 

12.56 

!45.24 

12.76 

47 

48 

46.33 

12.42 

! 46.31 

12.63 

46.25 

12.83 

46.20 

13.03 

48 

49 

47.33 

12.68 

47.27 

12.89 

47.22 

13.09 i! 47.16 

13.30 

49 

50 

48.30 

12.94 

48.24 

13.15 

1 48.18 

13.3G 

|49.12 

13.57 

50 

d 

« 

c 

j Dep. 

j Lat. 

Dep. 

Lat 

| Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

c 

ci 

Cfi 
• —1 

G 

1 - 
ID 

Dog. 

II 

! 74| Deg. 

i 

74*- 

j 

Deg. 

741 Deg. 

cJ 

+-> 

Ob 

Q 









































































































TKAVEKSE TABLE. 




o 

H • 

GO 

P 

15 Deg. 

15^ Deg 

15^ 

Deg. 

l5j Deg. 

1 

O 

1 — . 

<sj 

r-t- 

a 

a 

n> 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

P 

o 

(t> 

51 

49.26 

! 13.20 

49.20 

13.41 

49.15 

13.63 

49.09 

13.84 

51 

52 

50,23 

13.46 

50.17 

13.63 

50.11 

13.90 

50.05 

14.11 

52 

53 

151.19 

113.72 

51.13 

13.94 

51.07 

14.16 

51.01 

14.39 

53 

54 

i52.16 

1 13.98 

52.10 

14.20 

52.04 

14.43 

51.97 

14.60 

54 

55 

i53 . 13 

14.24 

53.06 

14.47 

53.00 

14.70 

52.94 

14.93' 

5.T 

56 

54.09 

114.49 

54.03 

14.73 

53.96 

14.97 

63.90 

15.20 

56 

57 

55.06 

: 14.75 

54.99 

14.99 

54.93 

15.23 

| 54.86 

15.47 

57 

58 

56.02 

15.01 

55.95 

15.26 

55.89 

15.50 

55.82 

15.74 

58 

59 

56.99 

|15.27 

56.92 

15.52 

56.85 

15.77 

56.78 

16.01 

59 

60 

57.96 

j15.53 

57.89 

15.78 

57.82 

16.03 

57.75 

16.29 

60 

61 

53.92 

15.79 

58.85 

16.04 

58.78 

16.30 

5S.71 

16.56 

61 

62 

59.89 

16.05 

59.82 

16.31 

59.75 

16.57 

59.67 

16.83 

02 

63 

60.85 

16.31 

60.78 

16.57 

60.71 

16.84 

60.63 

17. 10 

63 

64 

61.82 

16.56 

I 61.75 

16.83 

61.67 

17.10 

61.60 

17.37 

64 

65 

62.79 

16.82 

i62.71 

17.10 

62.64 

17.37 

62.56 

17.64 

65 

2 6 

63.75 

17.08 

■ 63.63 

17.35 

63.60 

17.64 

03.52 

17.92 

66 

67 

64.72 

17.34 

61.64 

17.62 

64.56 

17.90 

64.48 

18.19 

67 

63 

65.68 

17.60 

!65.61 

17.89 

65.53 

18.17 

65.45 

18.46 

63 

69 

66.65 

17.86 

!66.57 

18.15 

66.49 

18.44 

66.41 

18.73 

69 

70 

67.61 

18.12 

!67.54 

18.41 

67.45 

18.71 | 

67.37 

19.00 

70 

71 

68 .53 

18.38 

; 68.50 

18.68 

68.42 

18.97; 

68.33 

19.27 

71 

72 

69.55 

18.63 

'69.46 

18.94 1 

69.38 

19.24 

69.30 

19.54 

72 

73 

70.51 

18.89 

70.43 

19.20 

70.35 

19.51 : 

70.26 

19.82 

73 

74 

71.48 

19.15 

71.39 

19.46 | 

71.31 

i 9.78 

71.22 

20.09 

74 

75 

72.44 

19.41 

72.36 

19.73 

72.27 

20.04 

72.18 

20.36 

75 

76 

73.41 

! 9.67 

73.82 

19.99 : 

73.24 

20.31 j 

73. 15 

20.63 

76 

77 

74.38 

19.93 

74.29 

20.25 1 
20.52 

74.20 
75.16 

20.58 

74.1! 

20.90 

77 

78 

75.34 

20.19 

75.25 

20.84 

75.07 

21.17 

78 

79 

76.31 

20.45 

76.22 

20.78 

76.13 

21.11 i 

76.03 

21.44 

79 

80 

77.27 

20.71 

77.18 

21.04 

77.09 

21.38 1 

77.00 

21.72 

80 

81 

78.24 

20.96 1 

78.15 

21.31 

78.05 

21 . 65 

77.95 

21.99 

.31 

82 

79.21 

21.22 j 

79.11 

21.57 - 

79.02 

21.91 

78.92 

22.26 

82 

83 

80.17 

21.48 

80.08 

21.83 

79.98 

22.18 

79.83 

22 .53 

83 

84 

81.14 

21.74 
22.00 j 

22.26 j 

81.04 

22.09 

80.94 

22.45 

80.85 

22.80 

84 

85 

82.10 

82.01 

22.36 

SI .91 

22.72 

81.81 

23.07 

85 

86 

83.07 

82.97 

22.62 

82.87 

22.98 

82.77 

23.34 

86 

87 

84.04 

4 >9 co i 

83.94 

22.88 

83.84 

23.25 

83.73 

23.62 

87 

88 

85.00 

22.78 1 

84.90 

23.15 

84.80 

23.52 

84.70 

23.89 

88 

89 

85.97 

23.03 1 

85.87 

23.41 

85.76 

23 . 78 

85 . 66 

24 . 16 

89 

90 i 

86 . 93 

23 . 29 | 

86.83 

23.67 

86 . 73 

24.05 

86 . 62 

24.43 

90 

91 | 

87.90 

23 . 55 } 

87.80 

23 . 94 

87.69 

24.82 

87.58 

24.70 

91 

92 | 

88.87 

23.81 ; 

88 . 76 { 

24 . 20 

88 . 65 

24 . 59 

88 . 55 

24.97 

92 

93 

89.83 

24.07 

89.73 

24.46 

89 . 62 

24 . 85 

89.51 

25.24 

93 

94 ! 

90.80 

24.33 

90 . 09 ' 

24.72 

90 . 58 

25. 12 

90.47 

OC GO 

X*') . . 6 - 

94 

95 ‘ 

91.76 

24.59 ! 

91.65 

24.99 

91 .54 

25.39 j 

91 .43 

25.79 

95 1 

86 ; 

92 73 

24.85 

92.62 i 

25.25 

92.51 

25.65 

92.40 

26.06 

96 i 

97 ; 

93 . 69 

25.11 

93.58 j 

25 . 51 

93.47 

25 . 92 j 

93 . 36 

26 . 33 

97 

98 

94.66 

25 . 36 

94 . 55 ! 

25.78 

94.44 

26.19 | 

94.32 

26 . 60 

93 

99 i 95.63 

25 . 62 

95.51 | 

26.04 

95.40 

26.46 

95 . 28 

26 . 87 

99 

100 

96 . 59 

25.88 

36.48 

25.50 

96.36 

26 . 72 

96 . 25 

27.14 

100 

. 

CU 

o 

d 

Dep. 

Lat. 

Cep. 

Lai. 

| 

Dep. 

Lat. 

Dep. 

Ij vlt* 

6 

rt 

.2 

G 

» 

1 

75 Deg. 

74f Deg. 

744 Deg. 

i 

74* Deg. 

cv 

•VJ 

l: 

Urn 











































































































4 


TRAVERSE TABLE. 


a 1 

CO 

e— 

16 Deg. 

16£ Deg. 

Deg. 

16| Deg. 

O 

<—• 

CO 

*“*■ 

pa ! 

C 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

£3 

O 

re 

• 

1 

0.96 

0.28 

0.96 

0.28 

0.96 

0 28 

0.96 

0.29 

1 

2 

1 92 

0.55 

1.92 

0.56 

1.92 

0.57 

1.92 

0.58 

2 

3 

2.88 

0.83 

2.88 

0.84 

2.88 

0.85 

2.87 

0.86 

3 

4 

3.85 

1.10 

3.84 

1.12 

3.84 

1.14 

3.83 

1.15 

4 

5 

4.81 

1.38 

4.80 

1.40 

4.79 

1.42 

4.79 

1.44 

5 

6 

5.77 

1.65 

5.76 

1.68 

5.75 

1.70 

5.75 

1.73 

G 

7 

0.73 

1.93 

6.72 

1.96 

6.71 

1.99 

6.70 

2.02 

7 

8 

7.69 

2.21 

7.68 

2.24 

7.67 

2.27 

7.66 

2.31 

8 

9 

8.65 

2.48 

8.64 

2.52 

8.63 

2.56 

8.62 

2.59 

9 

10 

9.01 

2.76 

9.60 

2.SO 

9.59 

2.84 

9.58 

2 .S8 

10 

11 

10.57 

3.03 

10.56 

3.08 

10.55 

3.12 

10.53 

3.17 

11 

12 

11.64 

3.31 

11.52 

3.36 

11.51 

3.41 

11.49 

3.46 

12 

13 

12.50 

3.58 

12.48 

3.64 

12.46 

3.69 

12.45 

3.75 

13 

14 

13.46 

3.86 

13.44 

3.92 

13.42 

3.98 

13.41 

4.03 

14 

15 

14.42 

4.13 

14.40 

4.20 

14.38 

4.26 

14.36 

4.32 

15 

16 

15.38 

4.41 

15.36 

4.48 

15.34 

4.54 

15.32 

4.61 

16 

17 

16.34 

4.69 

16.32 

4.76 

16.30 

4.83 

16.28 

4.90 

17 

18 

17.30 

4.96 

17.28 

5.04 

17.26 

5.11 

17.24 

5.19 

18 

19 

18.26 

5.24 

18.24 

5.32 

18.22 

5.40 

18.19 

5.48 

19 

20 

19.23 

5.51 

19.20 

5.60 

19.18 

5.68 

19.15 

5.76 

20 

! 21 

20.19 

5.79 

20.16 

5.88 

20.14 

5.96 

20.11 

6.05 

21 

j 22 

21.15 

6.06 

21.12 

6.16 

21.09 

6.25 

21.07 

6.34 

22 

23 

22.11 

6.34 

22.08 

6.44 

22.05 

6.53 

22.02 

6.63 

23 

24 

23.07 

6.62 

23.04 

6.72 

23.01 

6.82 

22.98 

G. 92 

24 

i. 25 

24.03 

6.89 

24.00 

7.00 

23.97 

7.10 

23.94 

7.20 

25 

1 26 

24.99 

7.17 

24.96 

7.28 

24.93 

7.38 

24.90 

7.49 

26 

\ 27 

25.95 

7.44 

25.92 

7.56 

25.89 

7.67 

25.85 

7.78 

27 

28 

26.92 

7.72 

26.88 

7.84 

26.85 

7.95 

26.81 

8.07 

28 

29 

27.83 

7.99 

27.84 

8.11 

27.81 

8.24 

27.77 

8.36 

29 

30 

28.84 

8.27 

28.80 

8.39 

28.76 

8.52 

28.73 

8.65 

30 

31 

29.80 

8.54 

29.76 

8.67 

29.72 

8 .SO 

29.68 

8.93 

31 

32 

30.76 

8.82 

30.72 

8.95 

30.68 

9.09 

30.64 

9.22 

32 

s 33 

31.72 

9.10 

31.68 

9.23 

31.64 

9.37 

31.60 

9.51 

33 

\ 34 

32.68 

9.37 

32.64 

9.51 

32.60 

9.66 

32.56 

9.80 

34 

\ 35 

33.64 

9.65 

33.60 

9.79 

33.56 

9.94 

1 33.51 

10.09 

35 

36 

34.61 

9.92 

34.56 

10.07 

34.52 

10.22 

34.47 

10.38 

36 

! 37 

35.57 

10.20 

35.52 

10.35 

35.48 

10.51 

35.43 

10.66 

37 

1 38 

36.53 

10.47 

36.48 

10.63 

36.44 

10.79 

36.39 

10.95 

38 

j 39 

37.49 

10.75 

37-44 

10.91 

37.39 

11 . 08 

| 37.35 

11 .24 

39 

40 

33.45 

11.03 

38.40 

11.19 

38.35 

11.36 

38.30 

11.53 

40 

! 41 

39.41 

11.30 

39.36 

11.47 

39.31 

11 .64 

39.26 

11.82 

! 41 

42 

40.37 

11.58 

40.32 

11.75 

40.27 

11.93 

40.22 

12.10 

I 42 

43 

44 
j 45 

41.33 

11.85 

41.28 

12.03 

41.23 

12.21 

41.18 

12.39 

1 43 

*42.30 

12.13 

42.24 

12.31 

42.19 

12.50 

42.13 

12.68 

i 44 

43.26 

12.40 

43.20 

12.59 

43.15 

12.78 

43.09 

12.97 

45 

46 

44.22 

12.68 

44.16 

12.87 

44.11 

13.06 

44.05 

13.26 

46 

47 

45.18 

12.95 

45.12 

13.15 

45.06 

13.35 

45.01 

13.55 

47 

48 

46.14 

13.23 

46.08 

13.43 

46.02 

13.63 

45.96 

13.83 

48 

49 

47.10 

13.51 

47.04 

13.71 

46.98 

13.92 

46.92 

14.12 

49 

50 

48.06 

13.78 

48.00 

13.99 

47.94 

14.20 

47.88 

14.41 

50 

k 

a> 

o 

r* 

Dep. 

Lit. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

CD 

O 

c 

rf 

*-> 

CG 

• H 

, ^ 

74 Deg. 

73| Deg. 

731 

Deg. 

734 

Deg. 

1 2 

Q 

i 


i 





























































































































TRAVERSE TABLtv 


36 


u 
>— • 

V) 

r+- 

P 

16 Deg. 

16} Deg. 

16*- 

Deg 

16| Deg. 

C 

ST 

e-+- 

3 

o 

a 

Lat. 

Dep. 

Lat. 

Dep. 

T „ 4 . 

Lat. 

Dep. 

Lat.. 

Dep. 

p 3 

3 

o 

a 

51 

49,02 

14.06 

48.96 

14.27 

48.90 

14.48 

48.84 

14.70 

51 

52 

49.99 

14.33 

49.92 

14.55 

49.86 

14.77 

49.79 

14.99 

52 

53 

50.95 

14.61 

50.88 

14.83 

50.82 

15.05 

50.75 

15.27 

53 

54 

51.91 

14.88 

51.84 

15.11 

51.78 

15.34 

51.71 

15.56 

54 

55 

52.87 

15.16 

52.80 

15.39 

52.74 

15.62 

52.67 

15.85 

55 

56 

53.83 

15.44 

53.76 

15.67 

53.69 

15.90 

53.62 

16.14 

56! 

57 

54.79 

15.71 

54.72 

15.95 

54.65 

16.19 

54.58 

16.43 

57 1 

58 

55.75 

15.99 

55.68 

16.23 

55.61 

16.47 

55.54 

16.72 

58 

59 

56.71 

16.26 

56 . 64 

16.51 

56.57 

16.76 

56.50 

17.00 

59 

60 

57.68 

16.54 

57.60 

16.79 

57.53 

17.04 

57.45 

17.29 

60 

61 

58.64 

16.81 

58.56 

17.07 

58.49 

17.32 

58.41 

17.58 

61 

62 

59.60 

17.09 

59.52 

17.35 

59.45 

17.61 

59.37 

17.87 

62 

63 

60.56 

17.37 

60.48 

17.63 

60.41 

17.89 

60.33 

18.16 

63 

64 

61.52 

17.64 

61.44 

17.91 

61.36 

18.18 

61.28 

18.44 

64 

65 

62.48 

17.92 

62.40 

18.19 

62.32 

18.46 

62.24 

18.73 

65 

66 

63.44 

18.19 

63.36 

18.47 

63.28 

18.74 

63.20 

19.02 

60 

67 

64.40 

18.47 

64.32 

18.75 

64.24 

19.03 

64.16 

19.31 

67 

68 

65.37 

18.74 

65.28 

19.03 

65.20 

19.31 | 

65.11 

19.60 

68 

69 

66.33 

19.02 

66.24 

19.31 

66.16 

19.60 j 

66.07 

19.89 

69 

70 

67.29 

19.29 

67.20 

19.59 

67.12 

19.88 1 

67.03 

20.17 

70 

71 

68.25 

19.57 

68. 16 

19.87 

68.08 

20.17 

67.99 

20.46 

71 

72 

69.21 

19.85 

69.12 

20.15 

69.03 

20.45 

68.95 

20.75 

72 

73 

70.17 

20.12 

70.08 

20.43 

69.99 

20.73 

69.90 

21.04 

73 

74 

71.13 

20.40 

71.04 

20.71 

70.95 

21.02 

70.86 

21.33 

74 

75 

72.09 

20.67 

72.00 

20.99 

71.91 

21.30 

71.82 

21 .61 

75 

76 

73.06 

20.95 

72.96 

21.27 

72.87 

21.59 

72.78 

21.90 

76 

77 

74.02 

21.22 

73.92 

21.55 

73.83 

21.87 

73.73 

22.19 

77 

78 

74.98 

21.50 

74.88 

21 .83 

74.79 

22.15 

■ 74.69 

22.48 

78 

79 

75.94 

21.78 ! 

75.84 

22.11 

75.75 

22.44 

75.65 

22.77 

79 

80 

76 . 90 

22 . 05 

76.80 

22.39 

76.71 

22.72 

70* 61 

23.06 

80 

81 

77.80 

22.33 j 

77.76 

22.67 

77.66 

23.01 

77.56 

23.34 

81 

82 

78.82 

22.60 

78.72 

22.95 

78.62 

23.29 

78.52 

23.63 

82 

83 

79.78 

22.88 

79 . 68 

23 . 23 

79 . 58 

23.57 

79.48 

23 . 92 

83 

84 

80.75 

23.15 

80.64 

23.51 j 

80 . 54 

23.86 

80.44 

24.21 

84 

85 

81.71 

23 . 43 j 

81.00 

23 . 79 

81.50 

24.14 

J 81.39 

24.50 

85 

86 

82.67 

23 . 70 
23.98 1 

82.56 

24 . 07 

i82.46 

24.43 

i 82.35 

24.78 

86 

87 

83 . 63 

83.52 

24.35 

jS3 • 42 

24.71 

; 83.31 

25.07 

87 

88 

84.59 

24 . 26 

84.48 

24 . 62 

'84.38 

24 . 99 

!84.27 

25.36 

88 

89 

85.55 

24.53 1 

85.44 

24.90 

85.33 

25.28 

85.22 

25.65 

89 

90 

86.51 

24.81 i 

86.40 

25.18 

86.29 

25.56 

86.18 

25.94 

90 

91 

87.47 

25.08 1 

8 7.36 

25.46 

87.25 

25.85 

!87.14 

26.23 

91 

92 

88.44 

25.36 

88.32 

25.74 

88.21 

26.13 

188.10 

26.51 

92 

93 

89.40 

25.63 | 

89.28 

26.02 

89.17 

26.41 

l89.05 

26.80 

*3 

94 

90.T6 

25.91 

90.24 

26.30 

90.13 

26.70 

i90.01 

27.09 

94 

95 

91 .32 

26.19 i 

91.20 

26.58 

91.09 

26.98 

|90.97 

27.38 

95 

96 j 92.28 

26.40 

92.16 

26.86 

92.05 

27.27 

91.93 

27.67 

90 

97 

93.24 

26.74 

93.12 

27.14 

93.01 

27.55 

|92.88 

27.95 

97 

98 

94.20 

27.01| 

94.08 

27.42 

93.96 

27.83 

93.84 

28.24. 

98 

99 

95.16 

27.29 ! 

95.04 

27.70 

94.92 

23.12 

94 .80 

28.53 

99 

100 

96.13 

27.56 | 

96.00 

27.98 

95.88 

28.40 

95.76 

28.82 

• 100 

o’ 

y 

c 

Dep. 

Lat. | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

g 

c 

wLi 

74 Deg. ! 

73f Deg. 

73} 

Deg; 

73} Deg. 

</j 

C 










































































































3G 


TRAVERSE TABLE 


Distance. 

17 Deg. 

17! Deg. 

_ 

17| Deg. | 

17! Deg. 

D 

ST 

C-* 

P-5 

J .<at. 

Dep. j 

Lat. 

Dep. 

Lat. ! 

Dep. 

Lat. 

Dep. 

o 

CD 

'■ 1 I 

0.96 

0.29 

0.95" 

0.30 

0.95 

0.30 

0.95 

0.30 

1 

O 

/V 

1.91 

0.58 

1.91 

0.59 

1.91 

0.60 

1.90 

0.61 

o 

M 

3 | 

2.87 

0.88 

2.87 

0.89 

2.86 

0.90 | 

2.86 

0.91 

3 

4 

3.83 

1.17 

3.82 

1.19 

3.81 

1.20 

3.81 

l 22 

4 

5 

1.78 

1.46 

4.78 

1 .48 

4.77 

1.50 

4.76 

1.52 

5 

6 

5.74 

1.75 

5.73 

1.73 

5.72 

1.80 

5.71 

1.83 

6 

7 

6.69 

2.05 

6.69 

2.08 

6.68 

2.10 

6.67 

2 13 

7 

8 

7.65 

2.34 

7.64 

2.37 

7.63 

2.41 

7.62 

2.44 

9 

9 

8.61 

2.63 

8.60 

2.67 

8.58 

2.71 

r 57 

2.74 

9 

10 

9.56 

2.921 

9.55 

2.97 

9.54 

3.01 

.52 

3.05 

10 

11 ! 

10.52 

3.22 

10.51 

3.26 

10.49 

3.31 i 

0.48 

3.35 

11 

12 

11.43 

3.51 

11.46 

3.56 1 

11.44 

3.61 

11.43 

3.66 

12 

13 

12.43 

3.80 

12.42 

3.85 1 

12.40 

3.“ i 

12.38 

3.96 

13 

14 

13.39 

• 4.09 

13.37 

4.15 

13.35 1 

4 .1 

13.33 

4.27 

14 

15 

14.34 

4.39 

14.33 

4.45 1 

14.31 j 

.51 

14.29 

4.57 

15 

16 

15.30 

4.68 

15.28 

4.74 

15.26 , 

4.81 

15.24 

4.88 

16 

17 

16.26 

4.97 

16.24 

6.04 

16.21 1 

5.11 

16.19 

5.18 

17 

18 

17.21 

5.26 

17.19 

5.34 

17.17 

5.41 

17.14 

5.49 

IS 

19 

18.17 

5.56 | 

18.15 

6 63 I 

18.12 

5.71 

18.10 

5.79 

19 

20 

19.13 

5.85 

19.10 

5.93 J 

19.07 

G.01 

19.05 

6.10 

20 

21 

20.08 

6.14 

20.06 

(5.23 

20.03 

6.31 

20.00 

6.40 

21 

22 

21.04 

6.43 | 

21.01 

0 62 i 

20.98 

6.62 | 

20.95 

6.71 

22 

23 

21.99 

6.72 

21.97 

6.82 I 

21.94 

6.92 

21.91 

7.01 

23 

24 

22.95 

7.02 1 

22.92 

7.12 

22.89 

7.22 

22.86 

7.32 

24 

25 

23.91 

7.31 

23.88 

7 41 

23.84 

7.52 j 
7.82 i 

23.81 

7.62 

25 

26 

24.86 

7.60 

24.83 

7.71 

24.80 

24.76 

7.93 

26 

27 

25.82 

7.89 

25.79 

8.01 J 

25.75 

8.12 

25.71 

8.23 

27 

28 

26 .78 

8.19 

26.74 

8.30 

26-70 

8.42 

>26.67 

8 .54 

28 

29 

27.73 

8.48 

27.70 

8.60 

27.66 

8.72 

j 27.62 

8.84 

29 

30 

28.69 

8 . ,77 

28.65 

8.90 

28.61 

9.02 

28.57 

9.15 

30 

31 

29.65 

9.06 

29.61 

9.19 

29.57 

9.32 

OQ KO 

9.45 

31 

32 

30.60 

9.36 

30.56 

9.49 

30.52 

9.62 

30.48 

9.76 

32 

33 

31 .56 

9.65 

31.52 

9.79 

31.47 

9.92 

31.43 

10.06 

33 

34 

32.51 

9.94 

32.47 

10.08 : 

32.43 

10.22 

32.38 

10.37 

34 

35 

33.47 

10.23 

i33.43 

10.38 

33.38 

10.52 

33.33 

10.67 

35 

36 

34.43 

1 10.53 

34.38 

10.68 

34.33 

10.83 

34.29 

j 10.98 

36 

37 

35.38 

j 10.82 

35.34 

10.97 

35.29 

11.13 

35 24 

11.28 

37 

38 

36.34 

11.11 

36.29 

11.27 

36.24 

11.43 

36.19 

11.58 

38 

39 

37.30 

i11.40 

37.25 

11.57 

37.19 

11.73 

37.14 

11.89 

39 

40 

38.25 

11 .69 

i38.20 
39.16 

11.86 

38.15 

12.03 

38.10 

12.19 

40 

41 

39.21 

11.99 

12.16 

39.10 

12.33 

39.05 

12.50 

41 

42 

!40.16 

12.28 

40.11 

12.45 

40.06 

12.63 

40.00 

12.80 

42 

43 

1 41.12 

12.57 

41.07 

12.75 

41.01 

12.93 

40.95 

13.11 

43 

44 

42.08 

12.86 

42.02 

13.05 

41.96 

13.23 

41.91 

! 13.41 

44 

45 

I 43.03 

13.16 

! 42.98 

13.34 

1 42.92 

13.53 

42.86 

13.72 

45 

46 

i 43.99 

13.45 

i 43.93 
! ! 44.89 

13.64 

43.87 

13.83 

43.81 

14.02 

46 

47 

44.95 

13.74 

13.94 

44.82 

14.13 

1 44.76 

14.33 

47 

48 

45.90 

14.03 

1 45.84 

14.23 

45.78 

14.43 

45.71 

14.63 

48 

49 

46.86 

14.33 

46.89 

14.53 

46.73 

14.73 

46.67 

14.94 

49 

50 

47.82 

14.62 

47.75 

14.83 

II 47.69 

15.04 

I 47.62 

|15.24 

50 

• 

0) 

o 

e 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

y 

c. 

d 

.2 

r 

i let 
< O 

| 

Denr. 

o 

72| Deg. 

7 2 \ 

Deg. 

72J Deg. 

ri 

CA 

Q 
























































































































TRAVERSE table 


3? 


u 

In' 

r* 

P 

17 Deg. 

17* Deg. 

17* 

Deg. 

l?l Deg. 

Distance. 

3 

o 

» 

Lat. 

Dep. 

Lat,. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

43.77 

14.91 

48.71 

15.12 

48.64 

15.34 

48.57 

15.55 

51 

5 ‘3 

49.73 

15.20 

49.66 

15.42 

49.59 

15.64 

49.52 

15.85 

52 

53 

50.68 

15.50 

50.62 

15.72 

50.55 

15.94 

50.48 

16.10 

53 

54 

51.64 

15.79 

51.57 

16.01 

51.50 

16.24 

51.43 

10.46 

54 

55 

52.60 

16.08 

52.53 

16.31 

52.45 

16.54 

52.38 

16.77 

55 

50 

53.55 

16.37 

53.48 

16.61 

53.41 

16.84 

53*. 33 

17.07 

56 

57 

54.51 

16.67 

54.44 

16.90 

54.36 

17.14 

54.29 

17.38 

57 

58 

55.47 

16.96 

55.39 

17.20 

55.32 

17.44 

55.24 

17.68 

58 

59 

56.42 

17.25 

56.35 

17.50 

56.27 

17.74 

56.10 

17.99 

59 

00 

57.38 

17.54 

*57.30 

17.79 

57.22 

18.04 

57.14 

18.29 

60 

61 

58.33 

17.83 

58.26 

13.09 j 

58.18 

18.34 

58.10 

18.60 

61 

62 

59.29 

18.13 

59.21 

18.39 

59.13 

18.64 

1 59.05 

13.90 

62 

63 

60.25 

18.42 

60.17 

13.68 

60.08 

18.94 

:60.00 

19.21 

63 

64 

61.20 

18.71 

61.12 

18.98 ! 

01.04 

19.25 1 

60.95 

19.51 

64 

65 

62.10 

19.00 

62.03 

19.28 

61.99 

19.55 

61.91 

19.82 

65 

66 

63.12 

19.30 

63.03 

19.57 i 

62.95 

19.35 | 

62.86 

20.12 

66 

67 

64.07 

19.59 

63.99 

19.87 j 

63.90 

20.15 

63.81 

20.43 

67 

68 

05.03 

19.88 

64.94 

20.16 i 

64,85 

20.45 64.76 

20.73 

68 

69 

65.90 

20.17 

65.90 

20.46 

65.81 

20 . 75 

65.72 

21.04 

69 

70 

66.94 

20.47 

66 .35 

20.76 

66 .73 

21.05 

66.67 

21.34 

70 

71 

67.90 

20.76 

67.81 

21.05 

67.71 

21.35 

67.02 

21 .65 

71 

72 

68.85 

21.05 

63.76 

21.35 

68.67 

21.65 

68.57 

21.95 

72 

73 

69.81 

21.34 

69.72 

21.65 

69.62 

21.95 ! 

69.52 

22.26 

73 

74 

70.77 

21.64 

70.67 

21.94 

70.53 

22.25 

70.4-8 

22.56 

74 

75 

71.72 

21.93 

71.63 

22.24 

71.53 

22.55 

71.43 

22.86 

75 

76 

72.68 

22.22 

72.53 

22.54 

72.43 

22.85 

72.38 

23.17 

76 

77 

73.64 

22.51 

73.54 

22.83 

1 73.44 

23.15 

73.33 

23.47 

77 

78 

74.59 

22. SO 

74.49 

23.13 

74.39 

23.46 

74.29 

23.78 

78 

79 

75.55 

23.10 

] 75.45 

23.43 

75.34 

23.76 

75.24 

24.03 

79 

80 

76.50 

23.39 

76.40 

23.72 

76.30 

24.06 

76.19 

24.39 

80 

81 

77.46 

23.68 

1 77.36 

24.02 

77.25 

24.36 

77.14 
78.10 

24.69 

81 

82 

78.42 

23.97 

78.31 

24.32 

78.20 

24.66 

25.00 

82 

83 

79.37 

24.27 

79.27 

24.61 

70.16 

25.96 

79.05 

25.30 

83 

84 

80.33 

24.56 

80.22 

24.91 

80.11 

25.26 

80.00 

25.61 

84 

85 

81.29 

24.85 

81.13 

25.21 

81.07 

25.56 

80.95 

25.91 

85 

86 

82.24 

25.14 

82.13 

25.50 

82.02 

25.86 

81.91 

26.22 

86 

87 

83.20 

25.44 

83.09 

25.80 

82.97 

26.16 

82.86 

26.52 

87 

88 

84.15 

25.73 

84.04 

26.10 

83.93 

26.46 

: S3 . 8 l 

26.83 

83 

89 

85.11 

26.02 

85.00 

26.39 

84.88 

26.76 

84.76 

27.13 

80 

90 

86.07 

26.31 

85.95 

26.69 

85.83 

27.06 

85.72 

27.44 

90 

91 

87.02 

26.61 

86.91 

26.99 

86 .79 

27.36 

86.67 

27.74 

91 

92 

87.98 

26.90 

87.86 

27 .*28 

87.74 

27.66 : 

87.62 

23.03 

92 

93 

88 .94 

27.19 

88.82 

*27.58 

83.70 

27.97 

88 .57 

28.35 

93 

91 

89.89 

27.48 

89.77 

27.87 89.65 

28.27 

89.53 

28.66 

94 

95 

99.85 

27.78 

90.73 

28.17 

90.60 

28.57 

90.48 

23.96 

95 

96 

91.81 

28.07 

,91.63 

28.47 

.91.56 

28.87 

91.43 

29.27 

C 6 

97 

92.76 

28.36 

92.64 

28.76 

192.51 

29.17 

92.33 

29.57 

97 

98 

93.72 

28.65 

93.59 

29.06 

i93.46 

29.47 

93.33 

20.88 

98 

99 

94.67 

23.94 

94.55 

29.36 

! 34.42 

29.77 

94.29 

30.18 

99 

100 

95.63 

29.24 

.95.50 

29.65 

j95.37 

30.07 

95.24 

30.49 

t—* 

c: 

1 o 

■ 

© 

© 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L fit. 

Dep. 

Lat. 

CD 

Q 

C 

*«-> 

OC 

Q 

73 Deg. 

i 

72? Deg. 

72} 

Deg. 

72? Deg. 

. 

Q 

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38 


TRAVERSE TAJT5LE. 


v> 

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i 131 

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T It A V FliSF, T ABI E . 


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53.73 

19.03 

53.65 

19.26 

57 

58 

54.84 

18.83 

54.76 

19.12 

54.67 

19.36 

54.59 

19.60 

58 

59 

'55.79 

19.21 

55.70 

19.45 

55.62 

19.69 

55.53 

19.94 

59 

60 

56.73 

19.53 

56.65 

19.78 

56.56 

20.03 

56.47 

20.27 

60 

61 

57.68 

19.86 

57.59 

20.11 

57.50 

20.36 

57.41 

20.61 

"ST 

62 

58.62 

20.19 

58.53 

20.44 

58.44 

20.70 

58.35 

29,95 

62 

63 

59.57 

20.51 

59.48 

20.77 

|59.39 

21 .03 

59.29 

21.29 

63 

64 

60.51 

20.84 

60.42 

21.10 

!60.33 

21.36 

60.24 

21.63 

. 64 

65 

61.46 

21.16 

61.37 

21.43 

'61.27 

21.70 

61.18 

21.96 

65 | 

66 

02.40 

21.49 

62.31 

21.78 

62.21 

22.03 

62.12 

22.30 

66 

67 

63.35 

21 .81 

63.25 

22.09 

63.16 

22.37 

63.06 

22.64 

67 

68 

64.30 

22.14 

64.20 

22.42 

!64.10 

22.70 

64.00 

22 .9S 

68 

69 

65.24 

22.40 

65.14 

22.75 

! 65.04 

23 . 03 

64.94 

23.32 

69 I 

70 

66.19 

22 . 79 

66.09 

23 . 08 

65.98 

23 . 37 

65.88 

23.65 

70 

71 

67.13 

23.12 

67.03 

23.41 

!66.93 

23.70 

66.82 

23.99 

71 

72 

68 . 03 

23.44 

67.97 

23 . 74 

67.87 

24.03 

67.76 

24.33 

72 

73 

69.02 

23 . 77 

68.92 

24.07 

68.81 

0.1 0 7 

*/'ir . i 

68 . 71 

24.67 

73 

74 

69.97 

24.09 

69.86 

24.40 

09 . 76 

24.70 

69.65 

25 .01 

74 

75 

70.91 

24.42 

70.81 

24 . 73 

70.70 

25.04 

70.59 

25 . 34 

75 

76 

71.80 

24.74 

71.75 

25 . 06 

71.64 

25 . 37 

71 .53 

25 . 63 

76 

77 

72.80 

25.07 

72.69 

25.39 

1 72.58 

25.70 

72.47 

26.02 

77 

78 

73.75 

25.39 

73.64 

25.72 

73.53 

20.04 

73.41 

26.36 

73 

79 

74.70 

25.72 

74.53 

26.05 

74.47 

26.37 

74.35 

26.70 

79 | 

80 

75.64 

26.05 

75.53 

26.33 

75.41 

26 .70 

75.29 

27.03 

80 

81 

76.59 

26.37 

76.47 

26.70 

76.35 

27.04 

76.24 

27.37 

81 

82 

77.53 

26.70 

77.42 

27.03 

77.30 

27.37 

77.18 

27.71 

82 

83 

78.48 

27.02 

73.36 

27.36 

78.24 

27.71 

78.12 

23.05 

83 

84 

79.42 

27.35 

79.30 

27.69 

79.18 

28.04 

|79.06 

28.39 

84 

85 

80.37 

27.67 

80.25 

28.02 

80.12 

28.37 

180.00 

23.72 

85 

86 

81.31 

23.00 

81.19 

28.35 

81 .07 

28.71 

j80.94 

29.06 

86 

87 

82.26 

28.32 

82.14 

28.68 

82.01 

29.04 

!81.88 

29.40 

87 

88 

83.21 

28.65 

83.08 

29.01 

92.95 

29.37 

|82.82 

29.74 

88 

89 

84.15 

28.98 

84.02 

29.34 

83.90 

29.71 

83.76 

30.07 

89 

90 

85. 10 

29.30 

84.97 

29.67 

84.84 

30.04 

84.71 

30.41 

90 

91 

86.04 

29.63 

85.91 

30.00 

85.78 

30.38 

85.65 

30.75 

91 

92 

86.99 

29 . 95 

86.86 

30.33 

86.72 

30.71 

86.59 

31.09 

92 

93 

87.93 

30.28 

87.80 

30.66 

87.67 

31 .04 

87.53 

31.43 

93 

94 

88.38 

30.60 

88 .74 

30.99 

88.61 

31.38 

88.47 

31.76 

94 

95 

89.82 

30.93 

89.69 

31.32 

89.55 

31.71 

89.41 

32.10 

95 

96 ! 

90.77 

31.25 

90.63 

31.65 

90.49 

32.05 

90.35 

32.44 

96 

97 ! 

91.72 

31 . 58 

91.58 

31.98 

91.44 

32.38 

91.29 

32.78 

97 

98 

92.66 

31.91 

92.52 

32.31 

92.38 

32.71 

92.24 

33.12 

93 

99 

93.61 

32.23 

93.46 

32.64 

93.32 

33.05 

93.18 

33.15 

99 

100 

94.55 

32.56 

94.41 

32.97 

94.26 

33.38 

94.12 

33.79 

100 

« 

y 

C l 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

r’* 

• - > 

1 * ! 

t__ 

71 Deg. 

70f Deg. 

704 Deg. 

■ 

70 J Dej. 

* 

-*-> 

CO 

3 




















































































































42 


TRAVERSE TA15LE. 


Distance. 

20 Deg. 

20} Deg. 

204 

Deg. 

20} Deg. 

Distance.1 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.94 

0.34 

0.94 

0.35 

0.94 

0. 

35 

0 

.94 

0.3t 

1 

2 

1.88 

0.6S 

1.S8 

0.69 

1.87 

0. 

70 

1 

.87 

0.71 

9 

•m 

3 

2.82 

1.03 

2.81 

1.04 

2.81 

1. 

05 | 

2 

.81 

1.06 

3 

4 

3.76 

1.37 

3.75 

1.38 

3.75 

1. 

40 i 

3 

.74 

1.42 

4 

5 

4.70 

1.71 

4.69 

1.73 

4.68 

1. 

75 1 

4 

.68 

1.77 

5 

G 

5.64 

2.05 

5.63 

2.08 

5.62 

2. 

10 

5 

.61 

2.13 

6 

7 

6.58 

2.39 

6.57 

2.42 

6.56 

2. 

45 

6 

.55 

2.48 

7 

8 

7.52 

2.74 

7.51 

2.77 

7.49 

2. 

80 

7 

.48 

2.83 

8 

9 

8.46 

3.08 

8.44 

3.12 

8.43 

3. 

15 

8 

.42 

3.19 

9 

10 

9.40 

3.42 

9.38 

3.46 

9.37 

3. 

50 

9 

.35 

3.54 

i0 

11 

10.34 

3.76 

10.32 

3.81 

10.30 

3. 

85 

10 

.29 

3.90 

11 

12 

11.28 

4.10 

11.26 

4.15 

11.24 

4. 

20 

11 

.22 

4.25 

12 

13 

12.22 

4.45 

12.20 

4.50 

12.18 

4. 

55 

12 

.16 

4.61 

13 

14 

13.16 

4.79 

13.13 

4.85 

13.11 

4. 

90 

13 

.09 

4.96 

14 

15 

14.10 

5.13 

14.07 

5.19 

14.05 

5. 

25 

14 

.03 

5.31 

15 

16 

15.04 

5.47 

15.01 

5.54 

14.99 

5. 

60 

14 

.96 

5.67 

16 

17 

15.97 

5.81 

15.95 

5.88 

15.92 

5. 

95 

15 

.90 

6.02 

17 

18 

16.91 

6.16 

16.89 

6.23 

16.86 

6. 

30 

16 

.83 

6.38 

18 

19 

17.85 

6.50 

17.83 

6.58 

17.80 

6. 

65 

17 

.77 

6.73 

19 

20 

18.79 

6.84 

18.76 

6.92 

18.73 

7. 

00 

18 

.70 

7.09 

20 

21 

19.73 

7.18 

19.70 

7.27 

19.67 

ry 

t . 

35 

19 

64 

7.44 

21 

22 

20.67 

7.52 

20.64 

7.61 

20.61 

7. 

70 

20 

.57 

7.79 

* * ; 

/W A* 

23 

21.01 

7.87 

21.58 

7.96 

21.54 

8. 

05 

21 

.51 

8.15 

23 

24 

22.55 

8.21 

22.52 

8.31 

22.48 

8. 

40 

22 

.44 

8.50 

24 

25 

23.49 

8.55 

23.45 

8.65 

23.42 

8. 

76 

23 

.38 

8.86 

25 

26 

24.43 

8.89 

24.39 

9.00 

24.35 

9. 

11 

24 

.31 

9.21 

26 

27 

25.37 

9.23 

25.33 

9.35 

25.29 

9. 

46 

25 

.25 

9.57 

27 

28 

26.31 

9.58 

26.27 

9.69 

26.23 

9. 

81 

26 

.18 

9.92 

28 

29 

27.25 

9.92 

27.21 

10.04 

27.16 

10. 

16 

27 

. 12 

10.27 

29 

30 

28.19 

10.26 

28.15 

10.38 

28.10 

10. 

51 

28 

.05 

10.63 

30 

31 

29.13 

10.60 

29.08 

10.73 

29.04 

10. 

86 

28 

.99 

10.98 

31 

32 

30.07 

10.94 

30.02 

11.08 

29.97 

11. 

21 

29 

.92 

11.34 

32 

33 

31.01 

11.29 

30.96 

11.42 

30.91 

11. 

56 

30 

.86 

11.69 

33 

34 

31.95 

11.63 

31.90 

11.77 

31.85 

11. 

91 

31 

.79 

12.05 

34 

35 

32.89 

11.97 

32.84 

12.11 

32.78 

12. 

26 

32 

.73 

12.40 

35 

36 

33.83 

12.31 

33.77 

12.46 

33.72 

12. 

61 

33 

.66 

12.75 

36 

37 

34.77 

12.65 

34.71 

12.81 

34.66 

12. 

96 

I 34 

.60 

13.11 

37 

38 

35.71 

13.00 

35.65 

13.15 

35.59 

13. 

31 

35 

.54 

13.46 

38 1 

39 

36.65 

13.34 

36.59 

13.50 

36.53 

13. 

66 

! 36 

.47 

13.82 

39 

40 

37.59 

13.68 

37.53 

13.84 

37.47 

14. 

01 

37 

.41 

14.17 

40 

41 

38.53 

14.02 

38.47 

14.19 

38.40 

14. 

36 

38 

.34 

14.53 

41 1 

42 

39.47 

14.36 

39.40 

14.54 

39.34 

14. 

71 

39 

.28 

14.88 

42 

43 

40.41 

14.71 

40.34 

14.88 

40.2S 

15. 

06 

40 

.21 

15.23 

43 

44 

41.35 

15.05 

41.28 

15.23 

41.21 

15 

41 

41 

.15 

15.59 

44 

45 

42.29 

15.39 

42.22 

15.58 

42.15 

15 

76 

42 

.08 

15.94 

45 

46 

43.23 

15.73 

43.16 

15.92 

43.09 

16 

11 

43 

.02 

16.30 

46 

47 

44.17 

16.07 

44.09 

16.27 

44.02 

16 

46 

| 43 

. 95 

16.65 

47 

48 

45.11 

16.42 

45.03 

16.61 

44.96 

16 

81 

144 

.89 

17.01 

48 

49 

146.04 

16.76 

45.97 

16.96 

45.90 

17 

.16 

45 

.82 

1 17.36 

49 

50 

46.98 

17.10 

46.91 

17.31 

46.83 

17 

.51 

46 

.76 

1 17.71 

50 

Distance.] 

Dep. 

1 Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

i Lat. 

Distance. 

70 Deg. 

69} Deg. 

694 Deg. 

69} Deg. 






































































































TKAVKKSK TABLE. 


43 


c 

5 

P 

20 Dog. 

20$ Deg. 

I 

*3 s 

z 

Deg. , 

20| Deg. 

O 

Cfl* 

3 

a 

o 

Lat. 

Dep. 

Lett* 

Dep. 

Lat. 1 

1 

Dep. 

Lat. 

Dep. 

P 

3 

CD 

CD 

51 

47.92 

17.44 

47.35 1 

17.65 

47.77 

17.86 

47.69 

18.07 

51 

52 

48.86 

17.79 

48.79 I 

18.00 

48.71 

18.21 

48.63 

18.42 

52 

53 

49.80 

18.13 

!49.72 1 

18.34 

49.64 

18.56 

49.56 

IS.78 

53 

54 

50.74, 

18.47 

j50.66 

18.69 

50.58 

18.91 

50.50 

19.13 

54 

55 

51.68 

18.81 

!51.60 

19.04 

51.52 

19.26 ; 

51.43 

19.49 

55 

56 

52.62 

19.15 

52.54 

19.38 

52.45 

19.61 1 

52.37 

19.84 

56 

57 

53.56 

19.50 

153.48 

19.73 

53.39 

19.96 i 

53.30 

20.19 

57 

58 

54.50 

19.84 

54.42 

20.07 

54.33 

20.31 ! 

54.24 

20.55 

58 

59 

55.44 

20.18 

j 55.35 

20.42 

55.26 

20.66 : 
21.01 ! 

55.17 

20.90 

59 

60 

56.38 

20.52 

! 56.29 

20.77 

56.20 

56.11 

21.26 

60 

61 

57.32 

20.86 

57.23 

21.11 j 

57.14 

21.36 1 

57.04 

21.61 

61 

62 

58.26 

21.21 

58. 17 

21.46 

58.07 

21.71 1 

57.98 

21.97 

62 

63 

59.20 

21.55 

59.11 

21.81 1 

59.01 

22.06 i 

j 58.91 

22.32 

63 

64 

60.14 

21.89 

60.04 

22.15 

59.95 

22.41 ! 

59.85 

22.67 

64 

65 

61.08 

90 99 

<-w -v • At rJ 

60.98 

22.50 j 

60.88 

22.76 1 

60.78 

23.03 

65 

66 

62.02 

22.57 

61.92 

22.84 

61.82 

23.11 1 

61 . 72 

23.38 

66 

67 

62.96 

22.92 

62.86 

23.19 ; 

62.76 

23.46 

62.65 

23.74 

67 

68 

63.90 

23.26 

63.80 

23.54 ; 

63.69 

23.81 1 

63.59 

24.09 

68 

69 

64.84 

23.60 

64.74 

23.88 ! 

;64.63 
65.57 

24.16 

64.52 

24.45 

69 

70 

65.78 

23.94 

65.67 

24.23 

24.51| 

65.46 

24.80 

70 

71 

66.72 

24.28 

66.61 

24.57 

66.50 

24.86 

66.39 

25.15 

71 

72 

67.66 

24.63 

67.55 

24.92 

67.44 

25.21 ! 

67.33 

25.51 

72 

73 

68.60 

24.97 

68.49 

25.27 

68.38 

25.57 

68.25 

25.86 

73 

74 

09.54 

25.31 , 

69.43 

25.61 

69.31 

25.92 

69.20 

26.22 

74 

75 

70.4-8 

25.65 

70.36 

25.96 

70.25 

26.27 

170.14 

26.57 

75 

76 

71.42 

25.99 

71.30 

26.30 

71.19 

26.62 

71.07 

26.93 

76 

77 

72.36 

26.34 

72 . 24 

26.65 

72.12 

26.97 

72.01 

27.28 

77 

78 

73.30 

26.68 I 

73.18 

27.00 

73.06 

27.32 

72.94 

27.63 

78 

79 

74.24 

27.02 - 

74.12 

27.34 

74.00 

27.67 

1 73.88 

27.99 

79 

80 

75.18 

27.36 

75.06 

27.69 

74.93 

28.02 

74.81 

28.34 

80 

81 

76.12 

27.70 

75.99 

28.04 

75.87 

2S.37 

75.75 

28.70 

81 

82 

77.05 

28.05 

76.93 

23.38 

76.81 

28.72 

76.68 

29.05 

82 

83 

77.99 

28.39 

77.87 

28.73 

77.74 

29.07 

77.62 

29.41 

83 

84 

78.93 

28.73 

78.81 

29.07 

78.68 

29.42 

78.55 

29.76 

84 

85 

79.87 

29.07 

79.75 

29.42 

79.62 

29.77 

79.49 

30.11 

85 

86 

80.81 

29.41 

80.63 

29.77 

80.55 

30.12 

80.42 

30.47 

86 

87 

81.75 

29.76 

81.62 

30.11 

81.49 

30.47 

81.36 

30.82 

87 

88 

82.69 

30.10 

82.56 

30.46 

82.43 

30.82 

82.29 

31.18 

SS 

89 

83.63 

30.44 

83.50 

30.80 

83.36 

31.17 

83.23 

31.53 

89 

90 

84.57 

30.78 

84.44 

31.15 

84.30 

31.52 

84.16 

31.89 

90 

91 

85.51 

31.12 

85.38 

31.50 

85.24 

31.87 

85.10 

32.24 

91 

92 

86.45 

31.47 

86.31 

31.84 

86.17 

32.22 

86.03 

32.59 

92 

93 

87.39 

31.81 

87.25 

32.19 

87.11 

32.57 

86.97 

32.95 

93 

94 

88.33 

32.15 | 

88.19 

32.54 

88.05 

32.92 

87.90 

33.30 

94 

95 

89.27 

32.49 

89.13 

32.88 

88.98 

33.27 

88.84 

33.66 

95 

96 

90.21 

32.83 

90.07 

33.23 

89.92 

33.62 

89.77 

34.01 

96 

97 

91.15 

33. I S 

91.00 

33.57 

90.86 

33.97 

90.71 

34.37 

97 

98 

92.09 

33.52 

91.94 

33.92 

91.79 

34.32 

91.64 

34.72 

98 

99 

93.03 

33.86 

92.88 

34.27 

92.73 

34.67 

92.58 

35.07 

99 

TOO 

93.97 

34.20 

93.82 

34.61 

93.67 

35.02 

93.51 

35.43 

100 

© 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

r* 

C£j 

♦-> 

a 

70 Deg. 

69f Deg. 

69 £ 

Deg. 

69^ Deg 

li 

! ~ 







































































































44 


TRAVERSE TABLE. 


o 

w’ 

p 

21 Deg. 

1 

21} Deg. 

t 

21' Deg. 

21} Deg. 

C 

b~ • 

l/. 

C+ 

p: 

3 

o 

p 

Lat. 

Dep. 

jL'dt. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

p 

1 

0.93 

0.36 

0.93 

0.36 

0.93 

0.37 

0.93 

0.37 

1 

2 

1.87 

0.72 

1.86 

0.72 

1.86 

0.73 

1.86 

0.74 

2 

3 

2.80 

1.08 

2.80 

1.09 

2.79 

1.10 

2/79 

1.11 

3 

4 

3.73 

1.43 

3.73 

1.45 

3.72 

1.47 

3.72 

1.48 

4 

5 

4.67 

1.79 

4.66 

1.81 

4.65 

1.83 

4.64 

1 .85 

5 

6 

5 • 60 

2.15 

5.59 

2.17 

5.58 

2.20 

5.57 

2.22 

6 

? 

6.51 

2.51 

0.52 

2.54 

6.51 

2.57 

6.50 

2.59 

7 

8 

7.47 

2.87 

7.46 

2.90 

7.44 

2.93 

7.43 

2.96 

8 

9 

8.40 

3.23 

8.39 

3.26 

8.37 

3.30 

8.36 

3.34 

9 

10 

9.34 

3.58 

9.32 

3.62 

9.30 

3.67 

9.29 

3.71 

10 

11 

10.27 

3.94 

10.25 

3.99 

10.23 

4.03 1 

10.22 

4.03 

11 

12 

11.20 

4.30 

11.18 

4.35 

11.17 

4.40 i 

11.15 

4.45 

12 ? 

13 

12.14 

4.66 

12.12 

4.71 

12.10 

4.76 

12.07 

1.82 

13 { 

14 

13.07 

5.02 

13.05 

5.07 

13.03 

5.13 i 

13.00 

5.19 

141 

15 

14.00 

5.39 l 

13.98 

5.44 

13.96 

5.50 ! 

13.93 

5.56 

15 

10 

14.94 

5.73 

14.91 

5.80 

14.89 

5.86 

14.86 

5.93 

16 

17 

15.87 

6.09 

15.84 

6.16 

15.82 

6.23 

15.79 

6.30 

17 

18 

16.80 

6.45 

16.78 

6.52 

16.75 

6.60 

16.72 

6.67 

13 

19 

17.74 

6.81 

17.71 

6.89 

17.68 

6.96 

17.65 

7.04 

19 

20 

19.67 

7.17 

18.64 

7.25 

18.01 

7.33 

18.53 

7.41 

20 

21 

19.61 

7.53 

19.57 

7.61 

19.54 

7.70 1 

19.50 

7.78 

O 1 

A* i 

99 

20.54 

7.88 

20.50 

7.97 

20.47 

8.06 I 

20.43 

8.15 

22 

23 

21.47 

8.24' 

21.44 

8.34 

21.40 

8.43 | 
8.80 1 

2 1 • 36 

8.52 

23 

24 

22.41 

8.60 

22.37 

8.70 

22.33 

9<> «>Q 

rw /V • iV i/ 

8.89 

24 

25 

23.34 

8.96 

23.30 

9.06 

23.28 

9.16 

23.22 

9.26 

25 

26 

24.27 

9.32 

24.23 

9.42 

24.19 

9.53 

24.15 

9.63 

26 

27 

25.21 

9.68 

25.16 

9.79 

25.12 

9 .98; 

25.08 

10.01 

27 

28 

26.14 

10.03 

26.10 

10.15 

26.05 

10.26 

26.01 

10 33 

28 

29 

27.07 

10.39 

27.03 

10.51 

26.98 

10.63 

26.94 

10.75 

29 

30 

28.01 

10.75 

27.96 

10.87 

27.91 

11.00 

27.86 

11.12 

30 

31 

28.94 

11.11 

23.89 

11.24 

28.84 

11.36 ! 

28.79 

11.49 

31 

32 

29.87 

11.47 

29.82 

11.60 

29.77 

11.73 

29.72 

11.86 

32 

33 

30.81 

11.83 

30.7.6 

11.96 i 

30.70 

12.09 

30.65 

12.23 

33 

34 

31.74 

12.18 

31.69 

12.32 

31.63 

12.48 

31.58 

12.60 

34 

35 

32.68 

12.54 

32.62 

12.69 

32.56 

12.83 ! 

32.51 

12.97 

35 

36 

33.61 

12.90 

33.55 

13.05 

33.50 

13.19 1 

33.44 

13.34 

36 

37 

34.54 

13.26 

34.48 

13.41 

34.43 

13.56 

34.37 

13.71 

37 

33 

35.48 

13.62 

35.42 

13.77 

35.36 

13.93 

35.29 

14.08 

33 

39 

36.41 

13.98 

36.35 

14.14 

36.29 

14.29 

36.22 

14.45 

39 

40 

37.34 

14.33 

37.28 

14.50 

37.22 

14.66 

37.15 

14.82 

40 

41 

38.28 

14.69 

38.21 

14.86 

38.15 

15.03 

38.08 

15.19 

41 

42 

39.21 

15.05 

39.14 

15.22 

39.08 

15.39 

39.01 

15.56 

42 

43 

40*14 

15.41 

40.08 

15.58 

40.01 

15.76 

39.94 

15.93 

43 

44 

41.08 

15.77 

41.01 

15.95 

40.94 

16.13 

40.87 

16.30 

44 

45 

42.01 

16.13 

41.94 

16.31 

41.87 

16.49 

41.80 

16.68 

45 

46 

42.94 

16.48 

42.87 

16.67 

42.80 

16.86 

42.73 

17.05 

46 

47 

43.88 

16.84 

43.80 

17.03 

43.73 

17.23 

43.65 

17.42 

47 

48 

44.81 

17.20 

44.74 

17.40 

44.66 

17.59 

44.58 

17.79 

48 

49 

45.75 

17.56 

45.67 

17.76 

45.59 

17.96 

45.51 

18.16 

49 

50 

46.68 

17.92 

46.60 

18.12 

46.52 

|18.33 

46.44 

18.53 

50 

• 

© 

© 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

! Lat. 

© 

o 

a 

! CJ 

69 Deo-. 

O 

63| Deg 

681 

Deg. 

63} Deg. 

«5 

ll 






























































































45 


* 


TKAVUIiSE table. 


cj 

* 

0* 

P 

J3 

1.0 

CD 

21 Deg. 

2D Deg. 

■ 

211 D »g- 

211 Deg. 

O 

Oi 

& 

►3 

O 

9 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i 

Dep. 

Lat. 

Dep. 

■ si 

47.61 

18.28 

47.53 

IS.48 

47.45 

18.69 

47.37 

18,90 

51 

52 

48.55 ! 

18.64 

48.46 

18.85 

48.38 ! 

19.06 

48.30 

19.27 

52 

53 

49.48 ; 

18.99 

49.40 

19,21 

49.31 

19.42 

49.23 

19.64 

53 

54 

50.41 i 

19.35 

50.33 

19.57 

50.24 | 

19.79 

50.16 

20.01 

54 

55 

51 35 j 

19.71 

51.26 

19.93 

51.17 ! 

20.16 

51.08 

20.38 

55 

56 

52 28 

20.07 

52.19 

20.30 

52.10 1 

20.52 

52.01 

20.75 

56 

57 

53 21 

20.43 

53.12 

20.66 

53.03 

20.89 

52.94 

21.12 

57 

58 

54.15 

20.79 

54.06 

21.02 

53.96 I 

21.28 

53.87 

21.49 

58 

59 

55.08 

21.14 

54.99 

21.38 

54.89 1 

21.62 

54.80 

21.86 

59 

GO 

56.01 

21.50 

55.92 

21.75 

55.83 

21.99 

55.73 

22.23 

60 

61 

56.95 

21.86 

56.85 

22.11 

56.76 

22.36 

56.66 

22,60 

61 

62 

57.88 

22.22 

57.78 

22.47 

57.69 

22.72 

57.59 

22.97 

62 

63 

58.82 

22.58 ! 

58.72 

22,83 

58.62 

23.09 

58.52 

23.35 

63 

64 

59.75 

22.94 ; 

59.65 

23.20 

59.55 

23.46 

59.44 

23.72 

64 

65 

60.68 

23.29 

60.58 

23.56 

60.48 

23.82 

60.37 

24.09 

65 

66 

61.62 

23.65 j 

61.51 

23.92 

G1.41 

24.19 

61.30 

24.46 

60 

67 

62.55 

24.01 ; 

62.44 

24.28 

62.34 

24.56 

62.23 

24.83 

67 

68 

63.48 

b* 

CO 

63.38 

24.65 

63.27 

24.92 

63.16 

25.20 

68 

69 

64.42 

24.73 

64.31 

25.01 

64.20 

25.29 

64.09 

25.57 

69 

70 

65.35 

25.09 

65.24 

25.37 

65.13 

25.66 

65.02 

25.94 

70 ! 

7) 

66.28 

25.44 

66.17 

25.73 

66.06 

26.02 

65.95 

26.31 

71 

72 

67.22 

25.80 

67.10 

26.10 

66.99 

26.39 

66.87 

26.68 

72 

73 

68.15 

26.16 

68.04 

26.46 

67.92 

26.75 

67.80 

27.05 

73 

74 

69.08 

26.52 

68.97 

26.82 

68.85 

27.12 

68.73 

27.42 

74 

75 

70.02 

20.83 

69.90 

27.18 

69.78 

27.49 

69.66 

27.79 

75 

76 

70.95 

27.24 

70.83 

27.55 

70.71 

27.85 

70T59 

28.16 

76 

77 

71.89 

27.53 

71.76 

27.91 

71.64 

28.22 

71.52 

28.53 

77 

78 

72.82 

27.95 

72.70 

28.27 

72.57 

28.59 

72.45 

28.90 

78 

79 

73.75 

28.31 

73.63 

28-. (33 

73.50 

28.95 

73.38 

29.27 

79 

80 

74.69 

28.67 

74.56 

29.00 

74.43 

29.32 

74.30 

29.64 

80 

81 

75.62 

29.03 

75.49 

29.36 

75.36 

29.69 

75.23 

30.02 

31 

82 

76.55 

29.39 

76.42 

29.72 

76.29 

30.05 

76.16 

30.39 

82 

83 

77.49 

29.74 

77.36 

30.08 

77.22 

30.42 

77.09 

30.76 

83 

84 

78.42 

30.10 

78.29 

30.44 

78.16 

30.79 

78.02 

31.13 

84 

85 

79.35 

30.46 

79.22 

30.81 

79.09 

31.15 

78.95 

31.50 

85 

86 

80.29 

30.82 

80.15 

31.17 

80.02 

31.52 

79.88 

31.87 

86 

87 

81.22 

31.18 

81.08 

31.53 

|80.95 

31.89 

80.81 

32.24 

87 

88 

82.16 

31 54 

82.02 

31.89 

!81.88 

32.25 

81.74 

32.61 

88 

89 

83.09 

31.89 

82.95 

32.26 

82.81 

32.62 

82.66 

32.98 

89 

90 

84.02 

32.25 

83.88 

32.62 

83.74 

32.99 

83.59 

33.35 

SO 

91 

84.96 

32.61 

84.81 

32.98 

84.67 

33.35 

84.52 

33.72 

91 

92 

85.89 

32.97 

85.74 

33.34 

85.60 

33.72 

85.45 

34.69 

92 

93 

86.82 

33.33 

86.68 

33.71 

86.53 

34.08 

S6.38 

34.46 

93 

94 

87.76 

33.69 

87.61 

34.07 

87.40 

34.45 

87.31 

34.83 

91 

95 

88.69 

34.04 

88.54 

34.43 

88.39 

34.82 

88.24 

35.20 

95 

96 

89.62 

34.40 

89.47 

34.79 

;89.32 

35.18 

89.17 

35.57 

96 

97 

90.56 

34.76 

90.40 

35.16 

| 90.25 

35.55 

90.09 

35.94 

97 

98 

91.49 

35.12 

91.34 

35.52 

;91.18 

35.92 

91.02 

36.31 

99 

99 

82.42 

35.48 

92.27 

35.88 

92.11 

36.28 

91.95 

36.69 

99 

100 

93.36 

35.84 

93.20 

36.24 

93.04 

36.65 

92.88 

37.08 

too 

V 

Dep. 

Lat. 

Dep. 

Lat. 

i Dep. 

Lat. 

Dep. 

Lat. 

<D 

O 

r-* 

.•i 

X 

£ 

60 Deg. 

68| Dog- 

! 081 

1 

Dog. 

1 

68 } Dog. 

cd 

C/3 

O 


22 





















































































































46 


TRAVERSE TABLE. 


* 


2 

S3 

<-*■ 

P 

22 Dog. 

22} Deg 

i 

22± 

Deg. 

22| Deg. 

"’i 

5 i 

w 

PS 

3 

O 

to 

• 

3 

o 

to 

• 

Lett. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

UTuiT 

0.37 

0.93 

0 

38 

0. 

92 

0.38 

0.92 

0.39 

1 

2 

1.85 

0.75 

1.85 

0. 

76 

1. 

85 

0.77 

1.84 

0.77 

2 

3 

2.78 

1.12 

2.78 

1 

14 

2. 

77 

1.15 

2.77 

1.16 

3 

4 

3.71 

1.50 

3.70 

1. 

51 

3. 

70 

1.53 

3.69 

' .55 

4 

5 

4.64 

1.87 

4.63 

1. 

89 

4. 

62 

1.91 

4.61 

i .93 

5 

6 

5.56 

2.25 

5.55 

o 

27 

5. 

54 

2.30 

5.53 

2.32 

6 

7 

6.49 

2.62 

6.48 

2. 

65 

6. 

47 

2.68 

6.46 

2.71 

7 

8 

7.42 

3.00 

7.40 

3. 

03 

7. 

39 

3.06 

7 38 

3.09 

8 

9 

8.34 

3.37 

8.33 

3. 

41 

8. 

31 

3.44 

8.30 

3.48 - 

9 

10 

9.27 

3.75 

9.26 

3. 

79 

9. 

24 

3.83 

9.22 

3.87 | 

10 

11 

10.20 

4.12 

10.18 

4. 

17 

10. 

16 

4.21 

10.14 

4.25 

11 

12 

11.13 

4.50 

11.11 

4. 

54 

11 

09 

4.59 i 

11.07 

4.64 

12 

13 

12.05 

4.87 

12.03 

4. 

92 

12. 

01 

4.97 ! 

11.99 

5.03 

13 

14 

12.93 

5.24 

12.96 

5. 

30 

12. 

33 

5.36 | 

12.91 

5.41 

14 

15 

13.91 

5.62 

13.88 

5. 

68 

13. 

86 

5.74 1 

13.83 

5.80 

15 

16 

14.S3 

5.99 

14.81 

6. 

06 

14. 

78 

6.12 1 

14.76 

6. 19 

16 

17 

15.76 

6.37 

15.73 

6. 

44 

15. 

71 

6.51 

15.68 

6.57 

17 

13 

16.69 

6.74 

16.66 

6. 

82 

16. 

63 

6.89 1 

16.60 

6.96 

18 

19 

17.62 

7. 12 

17.59 

7. 

19 

17. 

55 

7.27 

17.52 

7.35 

19 

20 

18.54 

7.49 

18.51 

7. 

57 

18. 

48 

7.65 

18.44 

7.73 

20 

21 

19.47 

7.87 

19.44 

7. 

95 

19. 

40 

8.04 

19.37 

8.12 

21 

22 

20.40 

8.24 

20.36 

8. 

33 

20. 

33 

8.42 

20.29 

8.51 

22 

23 

21.33 

8.62 

21.29 

8. 

71 

21 

25 

8.80 

21.21 

8.89 

23 

24 

22.25 

8.99 

22.21 

9. 

09 

22 

17 

9.18 

22. 13 

9.28 

24 

25 

23.18 

9.37 

23.14 

9. 

47 

23 

10 

9.57 

23.05 

9.67 

25 

26 

24.11 

9.74 

24.06 

9 

84 

24 

02 

9.95 

23.98 

10.05 

26 

27 

25.03 

10.11 

24.99 

10 

22 

24 

94 

10.33 

24.90 

10.44 

27 

28 

25.96 

10.49 

25.92 

10 

60 

25 

87 

10.72 j 

25.82 

10.83 

28 

20 

26.89 

10.88 

26.84 

10 

98 

26 

79 

11.10 

26.74 

11.21 

29 

30 

27.82 

11.24 

27.77 

11 

38 

27 

72 

11.48 

1 27.67 

11.60 

30 

31 

28.74 

11.61 

28.69 

11 

74 

28 

.64 

11.86 

28.59 

11.99 

31 

32 

29.67 

11.99 

29.62 

12 

12 

29 

.56 

12.25 

29.51 

12.37 

32 

33 

30.60 

12.38 

30.54 

12 

.50 

30 

.49 

12.63 

30.43 

12.76 

33 

34 

31.52 

12.74 

31.47 

12 

87 

31 

.41 

13.01 

131.35 

13.15 

34 

35 

32.45 

13.11 

32.39 

13 

.25 

32 

.34 

13.39 

i32.28 

13.53 

35 

36 

33.33 

13.49 

33.32 

13 

.63 

33 

.26 

13.78 

33.20 

13.92 

36 

37 

34.31 

13.86 

34.24 

14 

.01 

34 

.18 

14.16 

34.12 

14.31 

37 

38 

35.23 

14.24 

35.17 

14 

.39 

35 

.11 

14.54 

35.04 

14.70 

38 

39 

36.16 

14.61 

36.10 

14 

.77 

36 

.03 

14.92 

35.97 

15.08 

39 

40 

37.09 

14.98 

37.02 

15 

.15 

36 

.96 

15.31 

36.89 

15.47 

40 

41 

33.01 

15.36 

37.95 

15 

.52 

37 

.88 

15.69 

37.81 

15.86 

41 

42 

38.94 

15.73 

38.87 

15 

,90 

33 

.80 

16.07 

38.73 

16.24 

42 

43 

39.87 

16.11 

39.80 

16 

.28 

39 

.73 

16.46 

39.65 

16.63 

43 

44 

40.80 

16.48 

40.72 

16 

.66 

40 

.65 

16.84 

40.58 

17.02 

44 

45 

41.72 

16.86 

41.65 

17 

.04 

41 

.57 

17.22 

41.50 

17.40 

45 

46 

42.65 

17.23 

42.57 

17 

.42 

12 

.50 

17.60 

42.42 

17.79 

46 

47 

43.58 

17.61 

43.50 

17 

.80 

43 

.42 

17.99 

43.34 

18.IS 

47 

48 

44.50 

17.98 

44.43 

18 

.18 

44 

.35 

18.37 

44.27 

18.56 

48 

49 

45.43 

18.36 

45.35 

18 

.55 

45 

.27 

18.75 

45.19 

18.95 

49 

60 

46.36 

18.73 

46.28 

18 

93 

46 

.19 

19.13 

46.11 

19.34 

50 

6 

o 

es 

CO 

' H 

Q 

Dep. 

Lett* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Distance, j 

68 Deg. 

67f Deg 


67^ Deg. 

67} Deg. 

1 


































































































































traverse table. 


•17 


: 

»— • 

Gfi 

<-► 

P 

22 Deg. 

o 

221 Deg 

• 

22A 

Deg 


221 Deg. 

! 

-j 

g 

35’ 

r** 

3 

O 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

3 

O 

G> 

51 

47 

.29 

19. 

10 

47 

.20 

19. 

31 

47 

.12 

19. 

52 

47 

.03 

19. 

72 

"51 

52 

48 

.21 

19. 

48 

48 

.13 

19. 

69 

48 

.04 

19. 

90 

47 

.95 

20. 

11 

52 

53 

49 

.14 

19. 

85 

49 

.05 

20. 

07 

48 

.97 

20. 

28 

48 

.88 

20. 

50 

53 

54 

50 

.07 

20. 

23 

49 

.98 

20. 

45 

49 

.89 

20. 

66 

49 

.80 

20. 

83 

54 

55 

51 

.00 

20. 

60 

50 

.90 

20. 

83 

50 

.81 

21. 

05 

50 

.72 

21. 

27 

55 

56 

51 

.92 

20. 

98 

51 

.83 

21. 

20 

51 

.74 

21. 

43 

51 

.84 

21. 

66 

56 

57 

52 

.85 

21. 

35 

52 

.76 

21. 

58 

52 

66 

21. 

81 

52 

.57 

22. 

04 

57 

58 

53 

. 78 

21. 

73 

53 

.68 

21. 

96 

53 

.59 

22. 

20 

53 

.49 

22. 

43 

58 

59 

54 

.70 

22. 

10 

54 

.61 

22. 

34 

54 

.51 

22. 

58 

54 

.41 

22. 

82 

59 

60 

55 

.63 

22. 

48 

55 

.53 

22. 

72 

55 

.43 

22. 

96 

55 

.33 

23. 

20 

60 

61 

56 

.56 

22. 

85 

56 

.47 

23. 

10 

56 

.36 

23. 

34 

56 

.25 

23. 

59 

61 

62 

57 

.49 

23. 

23 

57 

.38 

23. 

48 

57 

.28 

23. 

73 

57 

.18 

23. 

98 

62 

63 

58 

.41 

23. 

60 

58 

.31 

23. 

85 

58 

.20 

24. 

11 

58 

.10 

24. 

36 

63 

64 

59 

.34 

23. 

97 

59 

.23 

24. 

23 

59 

.13 

24. 

49 

59 

.02 

24. 

75 

64 

65 

60 

.27 

24. 

35 

60 

. 16 

24. 

61 

60 

.05 

24. 

87 

59 

.94 

25. 

14 

65 

66 

61 

.19 

24. 

72 

61 

.09 

24. 

99 

60 

.98 

25. 

26 

60 

.87 

25. 

52 

66 

67 

62 

.12 

25. 

10 

62 

.01 

25. 

37 

61 

.90 

25. 

64 

61 

.79 

25. 

91 

07 

68 

63 

.05 

25 

47 

62 

.94 

25. 

75 

62 

.82 

26. 

02 

62 

.71 

26. 

30 

68 

69 

63 

.98 

25. 

85 

63 

.86 

26. 

13 

63 

.75 

26. 

41 

03 

.63 

26. 

68 

69 

70 

64 

.90 

26. 

22 

64 

.79 

26. 

51 

64 

.67 

26. 

79 

64 

.55 

27. 

07 

70 

71 

65 

.83 

26. 

60 

65 

.71 

26. 

88 

65 

.60 

27. 

17 

65 

.48 

27. 

40 

71 

72 

66 

.76 

26. 

97 

66 

.64 

27. 

26 

66 

52 

27. 

55 

66 

.40 

27. 

84 

72 

73 

67 

.68 

27. 

35 

67 

.56 

27. 

64 

67 

.44 

27. 

94 

07 

.32 

28. 

23 

73 

74 

68 

.61 

27. 

72 

68 

.49 

28. 

02 

68 

.37 

28. 

32 

68 

.24 

28. 

62 

74 

75 

69 

.54 

28. 

10 

69 

.42 

28. 

40 

69 

.29 

23. 

70 

69 

. 17 

29. 

00 

75 

76 

70 

.47 

28. 

47 

70 

.34 

28. 

78 

70 

.21 

29. 

08 

70 

.09 

29. 

39 

76 

77 

71 

.39 

28. 

84 

71 

.27 

29. 

16 

71 

.14 

29. 

47 

71 

.01 

29. 

78 

77 

78 

72 

.32 

29. 

22 

72 

.19 

29. 

53 

72 

.06 

29. 

85 

1 71 

.93 

30. 

16 

78 

79 

73 

.25 

29. 

59 

73 

.12 

29. 

91 

72 

.99 

30. 

23 

72 

.85 

30. 

55 

79 

80 

74 

.17 

29. 

97 

74 

.04 

30. 

29 

73 

.91 

30. 

61 

73 

.78 

30. 

94 

80 

81 

75 

.10 

30. 

34 

74 

.97 

30. 

67 

74 

.83 

31 

00 

74 

.70 

31. 

32 

81 

82 

76 

.03 

30. 

72 

75 

.89 

31. 

05 

75 

.76 

31 

38 

75 

.62 

31. 

71 

82 

83 

76 

.96 

31. 

09 

76 

.82 

31. 

43 

76 

.68 

31. 

76 

76 

.54 

32. 

10 

83 

84 

77 

.88 

31. 

47 

77 

.75 

31 . 

81 

77 

.61 

32. 

15 

77 

.46 

32. 

48 

84 

85 

78 

.81 

31. 

84 

78 

.67 

32. 

19 

78 

.53 

32. 

53 

78 

.39 

32. 

87 

85 

86 

79 

.74 

32. 

22 

79 

.60 

32. 

56 

79 

.45 

32. 

91 

79 

.31 

33. 

26 

86 

87 

80 

.66 

32. 

59 

SO 

.52 

32. 

94 

80 

.38 

33. 

29 

80 

.23 

33. 

64 

87 

88 

81 

.59 

32. 

97 

81 

.45 

33. 

32 

81 

.30 

33. 

68 

81 

.15 

34. 

03 

88 

89 

82 

.52 

33. 

34 

82 

.37 

33. 

70 

82 

.23 

34. 

06 

82 

.08 

34. 

42 

89 

90 

83 

.45 

33. 

71 

83 

.30 

34. 

08 

83 

.15 

34. 

44 

83 

.00 

34. 

30 

90 

91 

84 

.37 

34. 

09 

84 

.22 

34. 

46 

84 

.07 

34. 

82 

83 

.92 

35. 

19 

91 

92 

85 

.30 

34. 

46 

85 

.15 

34. 

84 

85 

.00 

35. 

21 

84 

.84 

35 

58 

92 

93 

86 

.23 

34. 

84 

86 

.08 

35. 

21 

85 

.92 

35. 

59 

85 

.76 

35. 

96 

93 

94 

87 

.16 

35. 

21 

87 

.00 

35. 

59 

86 

.84 

35. 

97 

86 

.69 

36. 

35 

94 

95 

88 

08 

35. 

59 

87 

.93 

35. 

9? 

87 

.77 

36. 

35 

87 

.61 

36. 

74 

95 

96 

89 

01 

35. 

96 

88 

.85 

36. 

35 

88 

.69 

36. 

74 

88 

.53 

37. 

12 

96 

97 

89 

94 

36. 

34 

89 

.78 

36. 

73 

89 

.62 

37. 

12 

89 

.45 

37 

51 

97 

98 

90 

86 

36. 

71 

90 

.70 

37. 

11 

90 

.54 

37. 

50 

90 

.38 

37. 

90 

98 

99 

91 

.79 

37. 

09 

91 

83 

37. 

49 

91 

.46 

37. 

89 

91 

.30 

38. 

28 

99 

iOO 

92 

72 

37. 

46 

92 

.55 

37. 

86 

92 

.39 

38. 

27 

92 

.22 

38. 

67 

100 

S3 j 
O 1 

C 

Dep. 

Lat. 

Dep. 

Lat. 

Den. 

Lat. 

Dep. 

Lat. 

* 

O 

V 

cd 

4-> 

68 Deg. 


671 Deg. 

G7| Deg 


67 J 

Dost 


1 

2 ! 

5 l 

j 





























































































13 


ITtAVEKSK TABLE. 


Distance. 

23 Deg. 

23i Deg. 

23-’,- Deg- 

231 Deg. 

Distance.' 

Lat. 

Dop. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.92 

0.39 

0.92 

0.39 

0.92 

0.40 j 

0.92 

0.40 

1 

o 

1.84 

0.78 

1.84 

0.79 

1.83 

0.80 

1.83 j 

0.81 

2 

3 ' 

2.76 j 

1.17 

2.76 

1.18 

2.75 

1.20 

2.75 i 

1.21 

3 

4 

3.68 | 

1.56 

3.68 

1.58 

3.67 

1.59 

3.66 

1.61 

4 

5 

4,30 

1.95 

4.59 

1.97 

4.59 

1.99 

4.58 i 

2.01 

5 

! 6 

5.52 ! 

2.34 

5.51 

2.37 

5.50 

2.39 

5.49 1 

2.42 

6 

7 ' 

6.44 i 

2 74 

6.43 

2.76 

6.42 

2.79 

6.41 | 

2.82 

7 

8 

7.36 j 

3.13 

7.35 

3.16 

7.34 

3.19 

7.32 

3.22 

8 

9 ! 

8.28 

3.52 

8.27 

3.55 

8.25 

3.59 

8.24 

3.62 

9 

10 | 

9.20 

3.91 

9.19 

3.95 

9.17 

3.99 

9.15 | 

4.03 

0 

11 

10.13 

4.30 

10.11 

4.34 

10.09 

4.39 

10.07 j 

4.43 

11 

12 

11.05 

4.69 

11.03 

4.74 

11.00 

4.78 

10.98 

4.83 

12 

13 

11.97 

5.08 

11.94 

5.13 

11.92 

5.18 

11.90 1 

5.24 

13 

14 

12.89 

5.47 

12.86 

5.53 

12.84 

5.58 

12.81 

5.64 

14 

15 

13.81 

5.86 

13.78 

5.92 

13.76 

5.98 

13.73 

6.04 

15 

16 

14.73 

6.25 

14.70 

6.32 

14.67 

6.38 

14.64 

6.44 

16 

17 

15.65 

6.64 

15.62 

6.71 

15.59 

6.78 

15.56 

6.85 

17 

18 

16.57 

7.03 

16.54 

7.11 

16.51 

7.18 

16.48 

7.25 

18 

19 

17.49 

7.42 

17.46 

7.50 

17.42 

7.58 

17.39 

7.65 

19 

20 

18.41 

7.81 

18.38 

7.89 

18.34 

7.97 

18.31 . 

8.05 

20 

21 

19.33 

8.21 

19.29 

8.29 

19.26 

8.37 

19.22 

8.46 

21 

22 

20.25, 

8.60 

20.21 

8.68 

20.18 

8.77 

20.14 

8.86 

oo 

•** 

23 

21.17 

8.99 

21.13 

9.08 

21.09 

9.17 j 

21.05 

9.26 

23 

24 

22.09 

9.38 

22.05 

9.47 | 

22.01 

9.57 1 

21.97 

9.67 

24 

25 

23.01 

9.77 

j 22.97 

9.87 

22.93 

9.97 

22.88 

10.07 

25 

26 

23.93 

i0. 16 

23.89 

10.26 

23.84 

10.37 

23.80 

10.47 

26 

27 

24.85 

.0.55 

24.81 

10.66 

24.76 

10.77 

!24.71 

10.87 

27 

28 

25.77 

.0.94 

25.73 

11.05 | 

25.68 

11.16 

25.63 

11.. 28 

28 

29 

26.69 

11.33 

26.64 

11.45 

26.59 

11.56 

126.54 

11.68 

29 

30 

27.62 

11.72 

27.56 

11.84 

27.51 

11.96 

27.46 

12,08 

30 

31 

28.54 

12.11 

28.48 

12.24 

28.43 

12.36 

28.37 

12.49 

31 

32 

29.46 

12.50 

29.40 

12.63 

29.35 

12.76 

29.29 

12.89 

a2 

33 

30.38 

12.89 

30.32 

13.03 

30.26 

13.16 

I 30.21 

13.29 

33 

34 

31.30 

13.28 

31.24 

13.42 

31.18 

13.56 

131.12 

13.69 

34 

35 

32.22 

13.68 

32.16 

13.82 

32.10 

13.96 

32.04 

14.10 

35 

36 

33.14 

14.07 

33.08 

14.21 

33.01 

14.35 

32.95 

14.50 

1 36 

37 

34.06 

14.46 

34.00 

14.61 

33.93 

14.75 

33.87 

14.90 

37 

38 

34.98 

14.85 

34.91 

15.00 

34.85 

15.15 

34.78 

15.30 

38 

39 

35.90 

15.24 

35.83 

15.39 

35.77 

15.55 

35.70 

15.71 

1 39 

40 

36.82 

15.63 

36.75 

15.79 

36.68 

15.95 

36.61 

16.11 

40 

41 

37.74 

16.02 

37.67 

16.18 

37.60 

16.35 

II 37.53 

16.51 

41 

42 

38.66 

10.41 

38.59 

16.58 

38.52 

16.75 

38.44 

16.92 

42 

43 

39.58 

16.80 

39.51 

16.97 

39.43 

17.15 

39.36 

17.32 

43 

44 

40.50 

17.19 

40.43 

17.37 

40.35 

17.54 

I! 40.27 

17.72 

44 

45 

1 41.42 

17.58 

41.35 

17.76 

41.27 

17.94 

41.19 

18.12 

45 

46 

42.34 

17.97 

42.26 

:18.16 

42.18 

18.34 

I 42.10 

18.53 

46 

47 

43.26 

18.36 

43.18 

18.55 

43.10 

18.74 

43.02 

18.93 

47 

48 

44.18 

18.76 

44.10 

18.95 

44.02 

19.14 

143.93 

19.33 

48 

49 

45.10 

19.15 

45.02 

19.34 

44.94 

1 19.54 

j 44.85 

19.73 

49 

50 

46.03 

19.54 

45.94 

19.74 

45.85 

I 19.94 

|j 45.77 

20.14 

50 

^1 — 1 »n 

Distanco. 

1 Dep. 

i_ 

Lat. 

Dep. 

Lat. 

Dep. 

i Lat. 

!| Dep. 

Lat. 

6 

o 

r* 

67 Deg 

66$ Deg. 

66* 

Deg. 

Ij 

664 Dog. 

d 

■*-> 

C/5 

Q 























































































































TRAVERSE TABLE 


19 


o 

u> 

«-*• 

P 

23 Deg. 

23\ Deg. 

23 k 

Deg. 

23^ Deg. 

O 

rn 

c— 

3 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

o 

o 

51 

46.95 

19.93 

46.86 

20. 13 

46.77 

20.34 

46.68 

20.54 

51 

52 

47 87 

20.32 

47.78 

20.53 

47.69 

20.73 

47.60 

20.94 

52 

53 

48.79 

20.71 

48.70 

20.92 

48.60 

21.13 

48.51 

21.35 

53 

54 

49.71 

21.10 

49.61 

21.32 

49.52 

21.53 

49.43 

21.75 

54 

55 

50.63 

21.49 

50.53 

21.71 

50.44 

21.93 

50.34 

22.15 

55 

56 

51.55 

21.88 

51.45 

22.11 

51.36 

22.33 

•51.26 

22.55 

56 

5? 

52.47 

22.27 

52.37 

22.50 

52.27 

22.73 

52. 17 

22.96 

57 

58 

53.39 

22.66 

53.29 

22.90 

53.19 

23.13 

53.09 

123.36 

58 

51) 

54.31 

23.05 

54.21 

23.29 

54.11 

23.53 

54 00 

23.76 

59 

66 

55.23 

23.44 

55.13 

23.68 

55.02 

23.92 

54.92 

24.16 

60 

61 

56.15 

23.83 

56.05 

24. OS 

55.94 

24.32 

55.83 

24.57 

61 

62 

57.07 

24.23 

56.97 

24.47 

56.86 

24.72 

56.75 

24.97 

62 

63 

57/99 

24.62 

57.88 

24.87 

57.77 

25.12 

57.66 

25.37 

63 

64 

58.91 

25.01 

58.80 

25.26 

53.69 

25.52 

58.58 

25.78 

64 

65 

59.83 

25.40 

59.72 

25.66 

59.61 

25.92 

59.50 

26.18 

65 

63 

60.75 

25.79 

60.64 

26.05 

60.53 

26.32 

60.41 

26.58 

68 

67 

61.67 

26.18 

01.56 

26 • 45 

61.44 

26.72 

61.33 

26.98 

67 

68 

62.59 

25.57 

62.48 

26.34 

62.36 

27.11 

62.24 

27.39 

68 

69 

63.51 

25.96 

63.40 

27.24 

63.28 

27.51 

i63.16 

27.79 

69 

70 

64.44 

27.35 

64.32 

27.63 

64. 19 

27.91 

|64.07 

28.19 

70 

71 

65.36 

27.74 

05.23 

23.03 

65.11 

23.31 

j 64.99 

28.59 

71 

3 72 

66.23 

28.13 

66.15 

28.42 

66.03 

23.71 

65.90 

29.00 

72 

73 

67.20 

28.52 

67.07 

28.82 

66.95 

29.11 

66.82 

29.40 

73 

74 

68. 12 

28.91 

67.99 

29.21 

67.86 

29.51 

67.73 

29.80 

74 

75 

69.04 

29.30 

68.91 

29.61 

63.78 

29.91 

|68.65 

30.21 

75 

76 

69.95 

29.70 

69.83 

30.00 

69.70 

30.30 

69.56 

30.61 

76 

77 

70.88 

30.09 

70.75 

30.40 

70.61 

30.70 

70.48 

31.01 

77 

78 

71.80 

30.48 

71.67 

30.79 

71.53 

31.10 

7! .39 

31.41 

78 

79 

72.72 

30.87 

72.58 

31.18 

72.45 

31,50 

72.31 

31.82 

79 

80 

73.64 

31 . 26 

73.50 

3T.5S 

73.36 

31.90 

73.22 

32.22 

80 

81 

74.56 

31.65 

74.42 

31.97 

74.28 

32.30 i 

74.14 

32.62 

81 

82 

75.48 

32.04 1 

75.34 

32.37 

75.20 

32.70 ! 

75.06 

33.03 

82 

83 

70.40 

32.43 | 

76.26 

32.76 

76.12 

33.10 1 

75.97 

33.43 

83 

84 

77.32 

32.82 I 

77.18 

33.16 

77.03 

33.49 1 

76.89 

33.83 

84 

85 

73.24 

33.21 i 

78.10 

33.55 

77.95 ; 

33.89 I 

77.80 

34.23j 

85 

86 

79.16 

33.60 

79.02 

33.95 

78.87 

34.29 

78.72 

34.64 

86 

87 

80.03 ! 

33.99 

79.93 

34.34 

79.78 i 

31.69 

79.63 

35.04 

87 

88 

81.00 J 

34.38 

80.85 

34.74 i 

80.70 ! 

35.09 

80.55 

35.44 ! 

88 

89 ! 

81.92 ! 

31.78 

SI .77 

35.13 ! 

81.62 ’ 

35.49 

81.46 

35.84 

89 

90 ( 

82.85 

35.17 

V.69 

35.53 

82.54 

35.89 

82.38 

36.25 

90 

91 

83.77 

35.56 

93.61 

35.92 

83.45 

36.29j 

83.29 

36.65 

91 

92 

84.69 

35.95 

84.53 

36.32 

8 4.37 

36.68 1 

84.21 

37.05 

92 

93 

85.61 

36.34 

85.45 

38.71 

85.29 

37.08 ; 

85.12 

37.46 

93 

94 

86.53 

36.73 

86.37 

37.11 

86.20 

37.48 i 

86.04 

37.86 

94 

95 

87.45 

37.12 

87.29 

37.50 

87.12 

37.83 - 

86.95 

38.26 

35 

96 

83.37 

37.51 

S3.20 | 

37.90 

88.04 

38.28 

87.87 

38.66 

98 

97 

89.29 

37.90 

89.12 | 

38 . 29 | 

88.95 

38 . 68 

88.79 

39.07 i 

97 

93 

90.21 

38.29 

90.04 

38.68 

89.87 

39.08 

89.70 

39.47 i 

98 j 

99 

91 . 13 

38 . 08 

90.96 

39.08 | 

90.79 

39.48 1 

90.62 

39.87 

99 | 

100 

92.05 

39.07 

91.88 

39.47 i 

91.71 | 

39.87 

91.53 

40 . 27 I 

100 

6 

a 

a 

Dep. 1 

Lat. 

Dep. 

Lat. 

Dep ) 

Lat. 

Dep 

Lat. | 

<z) 8 

O K 

c I 

d 

w 

* rH I 

3 1 

67 Deg. 

66f Deg. 

1 

06£ Deg. 

66i 

Deg. | 

i 

cS g 

•c-J 1 

pH l 

^ * 

—J 














































































































50 


TRAVERSE TABLE 


e 
*— • 

P 

a 

o 

o 

• 

24 Deg. 

24| Deg. 

a. a 2 

Deg. 

24f Deg. 

e 

CO 

c-*- 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

o 

CD 

i 

0.91 

0.41 

0.91 

0.41 

0.91 

0.41 

0.91 

0.42 

I 

2 

1.83 

0.81 

1.82 

0.82 

1.82 

0.83 

1.82 

0.84 

2 

3 

2.74 

1.22 

2.74 

1.23 

2.73 

1.24 

2 72 

1.26 

3 

4 

3.65 

1.63 

3.65 

1.64 

3.64 

1.66 

3.63 

1.67 

4 

5 

4.57 

2.03 

4.56 

2.05 

4.55 

2.07 

4.54 

2.09 

5 

G 

5.48 

2.44 

5.47 

2.46 

5.46 

2.49 j 

5.45 

2.51 

6 

7 

6.39 

2.85 

6.33 

2.87 

6.37 

2.90 

6.36 

2.93 

7 

S 

7.31 

3.25 

7.29 

3.29 

7.28 

3.32 

7.27 

3.35 

8 

9 

8.22 

3.66 

8.21 

3.70 

8.19 

3.73 

8.17 

3.77 

9 

10 

9.14 

4.07 

9.12 

4.11 

9.10 

4.15 

9.08 

4.19 

r0 

11 

10.05 

4.47 

10.03 

4.52 

10.01 

4.56 

9.99 

4.61 

ii 

12 

10.96 

4.88 

10.94 

4.93 

10.92 

4.98 

10.90 

5.02 

12 

13 

11.88 

5.29 

11.85 

5.34 

11.83 

5.39 

11.81 

5.44 

13 

14 

12.79 

5.69 

12.76 

5.75 

12.74 

5.81 

12.71 

5.86 

14 

15 

13.70 

6.10 

13.68 

6.16 

13.65 

6.22 

13.62 

6.28 

15 

16 

14.62 

6.51 

14.59 

6.57 

14.56 

6.64 

14.53 

6.70 

16 

17 

15.53 

6.92 

15.50 

6.98 

15.47 

7.05 

15.44 

7.12 

17 

18 

16.44 

7.32 

16.41 

7.39 

16.38 

7.46 

16.35 

7.54 

18 

19 

J7.36 

7.73 

17.32 

7.80 

17.29 

7.88 

17.25 

7.95 

19 

20 

18.27 

8.13 

18.24 

8.21 

18.20 

8.29 

18.16 

8.37 

20 

21 

19.18 

8.54 

19.15 

8.63 

19.11 

8.71 

19.07 

8.79 

21 

22 

20.10 

8.95 

20.06 

9.04 

20.02 

9.12 

19.98 

9.21 

22 

23 

21.01 

9.35 

20.97 

9.45 

20.93 

9.54 

20.89 

9.63 

23 

24 

21.93 

9.76 

21.88 

9.86 

21.84 

9.95 

21.80 

10.05 

24 

25 

22.84 

10.17 

22.79 

10.27 

22.75 

10.37 

22.70 

10.47 

25 

26 

23.75 

10.58 

23.71 

10.68 

23.66 

10.78 

23.61 

10.89 

26 

27 

24.67 

10.98 

24.62 

11.09 

24.57 

11.20 

24.52 

11.30 

27 

28 

25.58 

11.39 

25.53 

11.50 

25.48 

11.61 

25.43 

11.72 

28 

29 

26.49 

11.80 

26.44 

11.91 

26.39 

12.03 

26.34 

12.14 

29 

30 

27.41 

12.20 

27.35 

12.32 

27.30 

12.44 

27.24 

12.56 

30 

31 

28.32 

12.61 

28.26 

12.73 

28.21 

12.80 

28.15 

12.98 

31 

32 

29.23 

13.02 

29.18 

13. 14 

29.12 

13.27 

29.06 

13.40 

32 

33 

30.15 

13.42 

30.09 

13.55 

30.03 

13.68 

29.97 

13.82 

33 

34 

31.06 

13.83 

31.00 

13.96 

30.94 

14. 10 

30.88 

14.23 

34 

35 

31.97 

14.24 

14.64 

31.91 

14.3S 

31.85 

14.51 

31.78 

14.65 

35 

36 

52.89 

32.82 

14.79 

32.76 

14.93 

32.69 

15.07 

36 

37 

33.80 

15.05 

33.74 

15.20 

33.67 

15.34 

33.60 

15.49 

37 

38 

34.71 

15.46 

34.65 

15.61 

34.58 

15.76 

34.51 

15.91 

38 

39 

35.63 

15.86 

35.56 

16.02 

35.49 

16.17 

35.42 

16.33 

39 

40 

36.54 

16.27 

36.47 

16.43 

36.40 

18.59 

36.33 

16.75 

40 

41 

37.46 

16.68 

37.38 

16.84 

37.31 

17.00 

37.23 

17.16 

41 

42 

38.37 

17.08 

33.29 

17.25 

38.22 

17.42 

38.14 

17.58 

42 

43 

39.28 

17.49 

39.21 

17.60 

39.13 

17.83 

39.05 

18.00 

43 

44 

40.20 

17.90 

40.12 

18.07 

40.04 

18.25 

39.96 

18.42 

44 

45 

41.11 

18.30 

41.03 

18.48 

40.95 

18.66 

40.87 

18.84 

45 

46 

42.02 

18.71 

41.94 

18.89 

41.86 

19.08 

41.77 

19.26 

46 

47 

42.94 

19.12 

42.85 

19.30 

42.77 

19.49 

42.68 

19.68 

47 

48 

43.85 

19.52 

43.76 

19.71 

43.08 

19.91 

43.59 

20.10 

48 

49 

44.76 

19.93 

44.68 

20.13 

44.59 

20.32 

44.50 

20.51 

49 

50 

45.68 

20.34 

45.59 

20.54 

45.50 

20.73 

45.41 

20.93 

50 

6 

£ 

Dep. 

Lat. 

Dep. 

L:it. 

Dep. 

Lat. 

Dep. 

Lat. 

o 

c 

*-> 

Si 

-i 

66 Door. 

3 

65f Deg. 

G51 

Dog. 

65 J 

Deg. 

d 

+2 

CO 

a 

















































































TRAVERSE TABTiE. 


51 


0 

►— 

tn 

r+ 

P 


24 Deg. 

* 

24^ Deg. 

24 4 Deg 

• 

24f Deg 


O 

H • 

c* 

W 

3 

a 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

0 

* 

51 

46 

.59 

20. 

74 

46. 

50 

20. 

95 

46. 

41 

21 . 

15 

46.32 

21. 

35 

51 

52 

47 

.50 

21. 

15 

47. 

41 

21. 

36 

47. 

32 

21. 

56 

47.22 

21. 

77 

52 

53 

48 

.42 

21. 

56 

48. 

32 

21. 

77 

48. 

23 

21. 

98 

48.13 

22. 

19 

53 

54 

49 

.33 

21. 

96 

49. 

24 

22. 

18 

49. 

14 

22. 

39 

49.04 

22. 

61 

54 

55 

50 

.24 

22. 

37 

50. 

15 

22. 

59 

50. 

05 

22. 

81 

49.95 

23. 

03 

55 

56 

51 

.16 

22. 

78 

51. 

06 

23. 

00 

50. 

96 

23. 

22 

50.86 

23. 

44 

56 , 

57 

52 

.07 

23. 

18 

51. 

97 

23. 

41 

51. 

87 

23. 

64 

51.76 

23. 

86 

57 

58 

52 

.99 

23. 

59 

52. 

88 

23. 

82 

52. 

78 

24. 

05 

52.67 

24. 

28 

58 

59 

53 

.90 

24. 

00 

53. 

79 

24. 

23 

53. 

69 

24. 

47 

53.58 

24. 

70 

59 

60 

54 

.81 

24. 

40 

j 54. 

71 

24. 

64 

54. 

60 

24. 

88 

54.49 

25. 

12 

60 

61 

55 

.73 

24. 

81 

! 55. 

62 

25. 

05 

55. 

51 

25. 

30 

55.40 

25. 

54 

61 

62 

56 

.64 

25. 

-y 

56. 

53 

25. 

46 

56. 

42 

25. 

71 

56.30 

25. 

96 

62 

63 

57 

. 55 

25. 

62 

. 57. 

44 

or; 

s/O « 

88 

57. 

33 

26. 

13 

57.21 

28. 

38 

63 

64 

58 

.47 

26. 

03 

- 1 

;> -. 

35 

26. 

29 

58. 

24 

26. 

54 

58.12 

26. 

79 

64 

65 

59 

.38 

26. 

44 

59 . 

26 

26. 

70 

59. 

15 

26. 

96 

59.03 

27. 

21 

65 

66 

60 

.29 

26. 

84 

60. 

i S 

27. 

11 

60. 

06 

27. 

37 

59.94 

27. 

63 

66 

67 

61 

.21 

27. 

25 

61. 

09 

27. 

52 

60. 

97 

27. 

78 

60.85 

28. 

05 

67 

68 

62 

.12 

27. 

66 

62. 

00 

27. 

93 

61. 

88 

28. 

20 

61.75 

28. 

47 

68 

69 

63 

.03 

28. 

06 

62. 

91 

28. 

34 

62. 

79 

28. 

61 

62.66 

28. 

89 

69 

70 

63 

.95 

23. 

47 

63. 

$2 

28. 

75 

63. 

70 

29. 

03 

63.57 

29. 

31 

70 

71 

64 

.NO 

28. 

88 

64. 

74 

29. 

16 

64. 

61 

29. 

44 

04.48 

29. 

72 

71 

72 

65 

.78 

20. 

28 

65. 

65 

29. 

57 

65. 

52 

29. 

86 

65.39 

30. 

14 

72 

73 

66 

.69 

29. 

69 

66. 

56 

29. 

98 

66. 

43 

30. 

27 

66.29 

30. 

56 

73 

74 

67 

.60 

30. 

10 

67. 

47 

30 

39 

67. 

34 

30. 

69 

67.20 

30. 

98 

74 

75 

68 

.52 

30. 

51 

68. 

38 

30. 

80 

68. 

25 

31. 

10 

| 68 . 11 

31 

40 

75 

76 

69 

.43 

30. 

91 

69. 

29 

31 

21 

69. 

16 

31. 

52 

|69.02 

31 

82 

76 

77 

70 

.34 

31 . 

32 

70. 

21 

31. 

63 

70 

07 

31. 

93 

!69.93 

32 

24 

77 

78 

71 

.26 

31 . 

73 

71. 

12 

04 • 

04 

70. 

98 

32. 

35 

70 . 84 

32 

66 

78 

79 

72 

. 17 

32. 

13 

72. 

03 

32. 

45 

71. 

89 

32. 

76 

, 71.74 

33 

07 

79 

80 

73 

.08 

32. 

54 

72. 

94 

32. 

86 

72. 

80 

33. 

18 

!72 . 65 

33 

49 

80 

81 

74 

.00 

32. 

95 

73 

85 

33. 

27 

73. 

71 

33. 

59 

73.56 

33 

91 

81 

82 

74 

.91 

33. 

35 

74. 

76 

33. 

68 

74. 

62 

34. 

00 

74.47 

34 

33 

82 

83 

75 

.82 

33. 

76 

75. 

68 

34 

09 

75 

53 

34. 

42 

75.38 

34 

75 

S3 

81 

76 

.74 

34. 

17 

76. 

59 

34. 

50 1 

78 

44 

34. 

83 

76.28 

35 

17 

84 

85 

77 

.65 

34. 

57 

77. 

50 

34. 

91 ' 

77. 

35 

35. 

25 

77.19 

35 

59 

85 

86 

78 

. 56 

31. 

98 

78. 

41 

35 

32 1 

78 

26 

35. 

66 

78.10 

36 

00 

86 

87 

7!) 

AS 

35. 

39 i 

79. 

32 

35. 

73 

79. 

17 

36. 

08 

79.01 

33 

42 

87 

88 

80 

.39 

35. 

79 I 

80. 

24 

36. 

14 

80. 

08 

36. 

49 

79.92 

36 

84 

88 

89 

8J 

.31 

36. 

20 ; 

81 

15 

36. 

55; 

80. 

99 

36. 

91 

80.82 

37 

26 

39 

90 

82 


86 • 

«! 

82. 

06 

36. 

90 1 

81 

90 

37. 

32 

81.73 

37 

68 

90 

91 

83 

7W 

37; 

01 

82 

97 

37. 

38 1 

82. 

81 

37. 

74 

82.64 

38 

.10 

91 

92 

84 

.05' 

37. 

42 

83 

S3 

37. 

79 

83. 

72 

33. 

15 

83.55 

38 

.52 

92 

93 

84 

96 

37. 

NO 

84. 

79 

38. 

20 

84. 

63 

38 

57 

84.46 

38 

94 

93 

84 

85 

87 

88 . 

09 

V. 

85. 

71 

38. 

61 

85. 

54 

38. 

98 

85.37 

39 

.35 

94 

95 

St 


38. 

64 | 

86. 

62 

39. 

02 

86 

45 

39. 

40 

86.27 

39 

•77 

95 

96 

87 

70 

39 . 

05 

87. 

53 

39. 

43 

87 

36 

39. 

81 

87.18 

40 

.19 

96 

97 

88 

. 01 

»> A 1 

45 

88. 

44 

39. 

84 

88. 

27 

40. 

23 

88.09 

40 

.61 

97 

98 

39 

.53 

39 

p/3: 

89. 

35 

40. 

25 

89. 

18 

40. 

64 

89.00 

41 

03 

98 

99 

90 

.44 

4 9. 

27 

90 

26 

40. 

66 

90. 

09 

41 

05 

89.91 

41 

45 

99 

xOO 

'll 

Jt) 

40. 

1,7 

91. 

18 

41. 

07 

91 

00 

41. 

47 

90.81 

41 

.87 

100 

w 

o 

a 

Dop. 

Lf*. 1 

Dep. 

L at * 

Dep. 

Lat. 

Dep. 

L 

[it* 

6 

c 

r* 

00 

•4 

\_ 


S6 Of <f, 

- 1 

65| Deg 

• 

6 

i 

5} 

Deg 

« 

65} Deg 


• 1 —« 

Q 










































































































m 


TRAVERSE TABLE. 


M 

c**- 

P 

O 

CD 

25 Deg. 

25:1 Deg. 

25$ Deg. 

251 Deg. 

O 

M 

r* 

& 

Lat. 

Dep. 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

p 

1 

0.91 

0.42 

O.SO 

0.43 ! 

0.90 

0.43 

0.90 

6.43 

1 

O 

A/ 

1.81 

0.85 

1.81 

0.85 

1.81 

0.86 

1.80 

0.87 

2 

3 

2.72 

1.27 

2.71 

1.28 

2.71 

1.29 

2.70 

1.30 

o 

<J 

4 

3.63 

1.69 

3.62 

1.71 

3.G1 

1.72 

3.60 

9 .74 

4 

5 

4.53 

2.11 

4.52 

2.13 

4.51 

2.15 I 

4.50 

2.17 

5 

r> 

5.44 

2.54 

5.43 

2.5G 

5.42 ! 

2.58 

5.40 

2.61 

6 

7 

6 .34 

2.96 

0.33 

2.99 

6.321 

3.01 

6.30 

3.04 

7' 

• 

8 

7.25 

3.38 

7.24 

3.41 

7.22 

3.44 

7.21 

3.48 

8 

9 

8.16 

3.80 

8.14 

3.84 

8.12 

3.87 

8.11 

3.91 

9 

10 

9.06 

4.23 

9.04 

4.27 

9.03 

4.31 

9.01 

4.34 

10 

11 

9.97 

4.65 

9.95 

4.69 

9.93 

4.74 

0.91 

4.78 

11 

12 

it >.38 

5.07 

10.85 

5.12 

10. S3 

5.17 

10.81 

5.21 

12 

13 

11.78 

5.49 

11.76 

5.55 

11.73 

5.60 

11.71 

5.65 

13 

14 

12.69 

5.92 

12.66 

5.97 

12.64 

6.03 

12.61 

6.08 

14 

15 

13.59 

6.34 

13.57 

6.40 

13.54 

6.48 : 

13.51 

6.52 

15 

16 

14.50 

0.76 

14.47 

6.83 

14.44 

6 .89 1 

14.41 

6 .95 

16 

17 

15.41 

7.18 

15.38 

7.25 

15.34 

7.32 

15.31 

7.39 

17 

18 

16.31 

7.61 | 

16.28 

7.68 

10.25 

7.75 j 

16.21 

7.82 : 

18 

19 

17.22 

8.03 

17.18 

8.10 

17.15 

8.18 1 

17.11 

8.25 j 

19 

‘20 

13.13 

8.45 

18.09 

8.53 

18.05 

8.61 1 

18.01 

8.69 

20 

~2T 

19.03 

8.87 

18.99 

8.96 

18.95 

9.04 | 

18.91 

9.12 : 

21 

oo 

Ar V 

19.94 

9.30 

19.90 

9.38 

19.86 

9.47 i 

19.82 

9.56 

22 

23 

20.85 

9.72 

20.80 

9.81 

20.76 

9.90 

20.72 

9.99 

OO 

x- O 

24 

21 .75 

10.14 

21.71 

10.24 

21.66 

10.33 

21.62 

10.43 

24 

25 

22.66 

10.57 

22.61 

10.66 

22.56 

10.76 

22.52 

10.86 1 

25 

26 

23.56 

10.99 

23.52 

11.09 

23.47 

11.19 

23.42 

11 .30 

26 

0*7 

24.47 

11.41 

24.42 

11.52 

24.37 

11.62 

24.32 

11.73 

27 

28 

25.38 

11.83 

25.32 

11.94 ! 

25.27 

12.05 

25.22 

12.16 

28 

29 

26.28 

12.26 

26.23 

12.37 

26.17 

12.4S 

26.12 

12.60 

29 

30. 

27.19 

12.68 

27.13 

12.80 1 

27.08 

12.92 1 

27.02 

13.03 

30 

31 

28.10 

13.10 

28.04 

13.22 

27.08 

] 3.35 

27.92 

13.47 

31 

32 

29.00 

13.52 

28.94 

13.65 

28.88 

13.78 

28.82 

13.90 

32 

33 

29.91 

13.95 

29.85 

14.08 

29.79 

14.21 1 

29.72 

14.34 

33 

34 

30.81 

14.37 

30.75 

14.50 

30.69 

14.64 

30.62 

14.77 

34 

OF. 

31.72 

14.79 

31.60 

14.93 

31.59 

15.07 

31.52 

15.21 

35 

30 

32.63 

15.21 

32.56 

15.36 

32.49 

15.50 

32.43 

15.64 

36 S 

37 

33.53 

15.64 

33.46 

15.78 

33.40 

15.93 

33.33 

16.07 

37 

38 

34.44 

16.06 

34.37 

16.21 

34.30 

16.36 

34.23 

16.51 

38 

39 

35.35 

16.48 

35.27 

10.64 

35.20 

16.79 

35.13 

16.94 

39 

40 

30.25 

16.90 

36.18 

17.06' 

36.10 

17.22 

36.03 

17.33 

40 

41 

37.16 

17.33 

37.08 

17.49 

37.01 

17.65 

|36.93 

17.81 

41 

42 

38.06 

17.75 

37.99 

17.92 

37.91 

18.08 

i 37.83 

18.25 

| 42 

43 

38.97 

18.17 

38.89 

18.34 

38.81 

18.51 

! 38.73 

18.68 

43 

44 

39.88 

18.60 

39.80 

18.77 

39.71 

18.94 

! 39.63 

19.12 

1 44 

45 

40.78 

19.02 

40.70 

19.20 

40.62 

19.37 

I 40.53 

19.55 

S 45 

46 

41.69 

19.44 

41.60 

19.62 

41.52 

ID.SO 

!41.43 

119.98 

1 46 

47 

12,60 

19.86 

42.51 

20.05 

42.42 

20.23 

j 42.33 

; 20.42 

47 

48 

43.50 

20.29 

43.41 

20.48 

43.32 

20.66 

143.23 

20 .8ft 

48 

49 

44.41 

20.71 

44.32 

20.90 

44.23 

21.10 

! 44.13 

21.20 

49 ! 

50 

45.32 

21.13 

45.22 

21.33 

45.13 

21.53 

45.03 

21.72 

50 

© 

o 

e 

Dcp. 

Lq.1* 

Dep. 

Lat. 

Dcp. 

Lat. 

Dep. 

Lat. 

© 

o 

c 

d 

4-3 

73 
• — « 

O 

65 Deg. 

84f Deg. 

i 

64$ Deg. 

1 

64$ Deg. 

CO 

I 

















































































































TRAVERSE TABLE 


53 


o 

rT 

25 Deg. 

25^ Deg. 

25^ Deg. 

25| Deg. 

O 
►— • 

Ul 

r*- 

zs 

rs 

n> 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

O 

fD 

51 

44.22 

21.55 

46.13 

21.75 

46.03 

21.96 

45.94 

22.16 

"51 

52 

47.13 

21.98 

47.03 

22.18 

46.93 

22.39 

46.84 

22.59 

52 

53 

48.03 

22.40 

47.94 

22.61 

47.84 

22,82 

47.74 

23.03 

53 

54 

48.94 

22.82 

48.84 

23.03 

48.74 

23.25 

48.64 

23.46 

54 

55 

49.85 

O O o A 
<4 tj • 

49.74 

23.46 

49.64 

23.68 

49.54 

23.89 

55 

56 

50.75 

23.67 

50.65 

23.89 

:50.54 

24.11! 

50.44 

24.33 

56 

57 

51.66 

24.09 

51.55 

24.31 

i51.45 

24.54 

51.34 

24.76 

57 

58 

52.57 

24.51 

52.46 

24.74 

52.35 

24.97 

52.24 

25.20 

58 

59 

53 47 

24.93 

53.36 

25.17 

53.25 

25.40 

53.14 

25.63 

59 

50 

54 38 

25.36 

54.27 

25.59 

54.16 

25.83 

54.04 

26.07 

60 

61 

55 • 28 

25.78 

55.17 

26.02 

55.06 

26.26 

54.94 

26.50 

61 

62 

56.19 

26.20 

56.08 

26.45 

55.96 

2-6.69 | 

55.8 i 

26.9 i 

62 

63 

57.10 

26 62 

56.98 

26.87 

56.86 

27.12j 

36. 7 4 

2/ 37 

63 

64 

58.00 

27.05 

57.89 

27.30 

57.77 

27.55 | 

57.64 

27.80 

64 

65 

58.9 l 

27.47 

58.79 

27.73 

58.67 

27.93 ! 

58.55 

28.24 

65 

66 

59.82 

27.89 

59.69 

23.15 

59.57 

23.41 | 

59.45 

28.67 

66 

67 

60.72 

28.32 

60.60 

28.58 

60.47 

23.84 

60.35 

29.11 

67 

68 

61.63 

28.74 i 

61.50 

29.01 

161.38 

29.27 I 

61.25 

29.54 

68 

69 

62.54 

29.16| 

62.41 

29.43 

62.28 

29.71 

62.15 

29.98 

69 

70 

03.44 

29.58 

63.31 

29.86 

63.18 

30.14 

63.05 

30.41 

70 

71 

04.35 

30.01 j 

64.22 

30.29 

164.08 

30.57 

63.95 

30.85 

71 

72 

65.25 

30.43 1 

65.12 

30.71 

|64.90 

31.00 

64.85 

31.28 

72 

73 

66.18 

30.85 ! 

66.03 

31.14 

;65.89 

31.43 I 
33.86 i 
32.29 

65.75 

31.71 

73 

74 

67.07 

31.27 

G6.93 

31.57 

i66.79 

66.65 

32.15 

74 

75 

67.97 

31.70 

67.83 

31.99 

1 67.69 

67.55 

32.58 

75 

76 

68.88 

32.12 

68.74 

32.42 

168.60 

32.72 

68.45 

33.02 

76 

77 

69.79 

32.54 

69.64 

32.85 

j69.50 

33.15 

69.35 

33.45 

77 

78 

70.69 

32.96 

70.55 

33.27 

! 70.40 

33.58 

70.25 

33.89 

78 

79 

71.60 

33.39 

71.45 

33.70 

71 .30 

34.01 

71.16 

34.32 

79 

80 

72.50 

33.81 

! 72.36 

34.13 

72.21 

34.44 

72.06 

34.76 

SO 

81 

73.41 

34.23 

73.26 

34.55 

73.11 

34.8/ 

72.90 

35.19 

81 

82 

74.32 

34.65 

74.17 

34.98 

74.01 

35.30 

73.86 

35.62 

82 

83 

75.22 

35. OS 

75.07 

35.41 

74.91 

35.73 

74.76 

38.06 

83 

84 

76.13 

35.50 

75.07 

35.83 

75.82 

36.18 

75.66 

36.49 

84 

85 

77.04 

35.92 

76.88 

36.26 

76.72 

36.59 

76.56 

36.93 

85 

86 

77.94 

36.35 

77.78 
j 78.69 

36.68 

77.62 

37.02 

177.46 

37.36 

86 

87 

78.85 

36.77 

37.11 

78.52 

37.45 

78.36 

37.80 

87 

88 

79.76 

37.19 

79.59 

37.54 

79.43 

37.88 

79.26 

38.23 

88 

89 

80.66 

37.61 

80.50 

37.96 

80.33 

38.32 

80.16 

38.67 

89 

90 

81.57 

38.04 

81.40 

38.39 

81.23 

38.75 

81.00 

30.10 

90 

' 91 

82.47 

38.46 

82.31 

38.82 

82.14 

39.18 

81.96 

39.53 

91 

92 

83.38 

38.88 

83.21 

39.24 

! 83.04 

39.61 

82.86 

39.97 

92 

93 

84.29 

39.30 

84.11 

39.67 i 83.94 

40.04 

83.76 

40.40 

93 

94 

85.19 

39.73 

85.02 

40.10 84.84 

40.47 

84.67 

40.84 

94 

95 

86.10 

40.15 

l85.92 

40.52 85.75 

40.90! 

85 57 

41.27 

95 

96 

87.01 

40.57 

1 86.83 

40.95 i 86.65 

41 .33 

86.47 

41.71 

96 

97 

87.91 

40.99 

! 87.73 

41.38 87.55 

41.76 

87.37 

42.14 

97 

98 

88 . 82 

41.42 

j88.64 

41.80 

88.45 

42.19 

88.27 

42.58 

98 

99 

89.72 

41.84 

89.54 

42.23 
42.66 , 

89.36 

42.62 

89.17 

43.01 

99 

,00 

90.63 

42.26 

90.45 

90.26 

43.05 

! 90.07 

,43.44 

100 

: 6 

Dep. 

Lat. 

Dep. 

Lat. 

1 

Dep. 

Lat. 

i 

Dep. 

j X_i iX t ■* 

6 

rj 

ei 

it. 

d 

X 

Q 

65 Deg. 1 

1 

64f Deg. 

! 

64Deg. 

64?- 

Deg. 








































































































54 


TRAVERSE TABLE. 


g 

5 

e-+ 

P 

* 26 Deg. 

26£ Deg. 

26 $ Deg. 

261 

Deg. | 

• 

O 
►—< • 

CO 

r-+ 

P 

3 

CD 

? 

I. at. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dtp. 

3 

o 

p 

1 

0, 90 

0-44 

0.90 

0.44 

0.89 1 

0.45 

0.80 

0.45 j 

1 

2 

1,80 

0.88 

1.79 

0.88 

1.79 ! 

0.89 

L?9 

0.90 

O 

-4 

3 

2.70 

1 .32 

2.69 

1.33 

2.68 

1.34 

2.68 

1 .303 1 

3 

4 

3.60 

1.75 

3.59 

1.77 

3.58 1 

1.78 

3.57 

1.80 

9 

5 

4.49 

2.19 

4.48 

2.21 

4.47 

2.23 

4.46 | 

O *•) ^ 

V . ^*9 t 

r 

G 

5.39 

2.63 

5.38 

2.65 

5.37 

2.68 

5.36 j 

2.70 j 

6 

7 

6.29 

3.07 

6.28 

3.10 

6.26 

3.12 

6.25 

3. 15 | 

7 

8 

7.19 

3.51 

7.17 

3.54 

7.16 

3.57 

7.14 

3.60! 

8 

9 

8.09 

3.95 

8.07 

3.93 

8.05 

4.02 

8.04 | 

4.05 

9 

10 

8.99 

4.38 

8.97 

4.42 

8.95 | 

4.46 

8.83 

4.50 

10 

11 

9.89 

4.82 

9.87 

4.S7 | 

9.84 

4.91 

9.82 

4.95 

11 

12 

10.79 

5.28 

10.76 

5.31 

10.74 

5.35 

10.72 

5.40 

12 

13 

11.68 

5.70 

11.66 

5.75 

11.63 

5.80 

11.61 

5.85 l 

13 

14- 

12.58 

6.14 

12.56 

6.19 

12.53 

6.25 

12.50 

6.30 

14 j 

15 

13.43 

6.58 

13.45 

6.63 

13.42 

6.69 

13.39 

6.75 

15 

16 

14.38 

7.01 

14.35 

7.08 

14.32 

7.14 

14.29 

7.20 

16 

17 

15.28 

7.45 

15.25 

7.52 

15.21 

7.59 

15. IS 

7.65 

17 

IS 

16.18 

7.89 

16.14 

7.96 

16.11 

8.03 

16.07 

8.10 

18 

19 

17.03 

8.33 1 

17.04 

8.40 

1 17.00 

8.48 

16.97 

8.55 

19 ! 

20 

17.98 

8.77 | 

17.94 

8.85 

| 17.90 

8.92 j 

17.86 

9. GO 

20 

21 

18.37 

9.21 I 

18.83 

9.29 

18.79 

9.37 i 

18.75 

9.45 

21 

22 

19.77 

9.64 

19.73 

9.73 

19.69 

9.82 

19.65 

9.90 

*>9 

23 

20.67 

10.08 

1 20.63 

10.17 

i 20.58 

10.26 : 

20.54 

10.35 

23 

24 

21.57 

10.52 

21.52 

10.61 

| 21.48 

10.71 

21.43 

10.80 

2 4 

25 

22.47 

10.96 

22.42 
j 23.32 

11.06 

t 22.37 

11.15 

; 22.32 

11.25 

25 

26 

23.37 

i 11.40 

11 ,50 

i 23.27 

11.60 

23.22 

11.70 

26 

27 

24.27 

11.84 

24.22 

11.94 

| 24.16 

12.05 

! 24.11 

12.15 

27 

23' 

25.17 

! 12.27 

I 25.11 

12.38 

25.08 

12.49 

; 25.00 

12.60 

28 

29 

26.08 

I 12.71 

i 26.01 

12.83 

25.95 

12.94 

25.90 

13.05 

29 

30 

26.96 

13.15 

I 26.91 

13.27 

26.85 

13.39 

26.79 

13.50 

30 

31 

27.86 

13.59 

27.80 

13.71 

27.74 

13.83 It 27.68 

13.05 

31 

32 

28.76 

14.03 

28.70 

14.15 

23.64 

14.28 

28.53 

14.40 

32 

33 

29.66 

14.47 

: 29.60 

14.60 

29.53 

14.72 

> 29.47 

; 14.85 

33 

34 

30.56 

14.90 

! 30.49 

15.04 

; 30.43 

15. 17 

| 30.36 

15.30 

34 

35 

31.46 

15.34 

i 31.39 

15.48 

1 31.32 

15.62 

31.25 

15.75 

35 

36 

32.36 

15.78 

32.29 

15.92 

1 32.22 

16.06 

32.15 

16.20 

36 

37 

33.26 

16.22 

1 33.18 

■ 16.36 

33.11 

!16.51 

,33.04 

!16.65 

37 

33 

34.15 

16.66 

34.03 

! 16.81 

31.01 

16.95 

:33.93 

j 17.10 

33 

39 

35.05 

17. 10 

34.93 

17.25 

1 31.90 

17.40 

1 34.83 

17.55 

39 

40 

35.95 

17.53 

35.87 

I 17.69 

j 35.80 

!17.85 

135.72 

1 3.00 

40 

41 

36.85 

17.97 

36.77 

IS. 13 

36.69 

; 13.29 

36.61 

! 1.45 

41 

42 

37.75 

18 .41 

37.67 

j IS.53 

37.59 

18.74 

37.51 

18.90 

42 

43 

33.65 

18.85 

38.57 

19.02 

! 38.43 

19.19 

33.40 

19.35 

93 

4-4 

39.55 

19.29 

39.46 

,19.46 

39.38 

19.63 

39.29 

19.80 

44 

45 

40.45 

19.73 

40.38 

19.90 

40.27 

20.08 

40.18 

20.25 

45 

46 

41 .34 

20.17 

41.26 

20.35 

41.17 

20.53 

41.08 

29.70 

46 

47 

42.24 

20.60 

42. ! 5 

20.79 

42.03 

20.97 

41.97 

21.15 

47 

48 

i 43. 14 

21.04 

43.05 

i 21.23 

42.96 

21.42 

42.86 

21 . 60 

43 

16 

44.04 

21.48 

43.95 

, 21.67 

43.85 

; 21.86 

43.76 

22.05 

43 

60 

; 14.94 

21.92 

44.84 

22 . 11 

44.75 

I 22.31 

44.05 

22.50 

50 

© 

c 

c 

' Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

| Lat. 

Dep. 

Lat. 

• 

© 

ss 

* r-4 

;3 

64 Deg 

o 

631 

i 

Deg. 

63.$ Deg. 

63* 

Deg. 

e} 

1 .2 

1 3 






























































































TRAVERSE TABLE 


55 


3) 

►- • 
’fl 
<—*■ 

P 

26 Deg. 

26}- Deg. 

28* 

Deg. 

26* 

Deg. 

1 Distance. 
3 . 

P 

o 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

>1 

45.84 

22.36 j 

45.74 

22.56 

45.64 

22.76 

45-51 

22796“ 

51 

52 

46.74 

22.80 1 

46.64 

23.00 

46.54 

23.20 

46.43 

23.41 

52 

52 

47.64 

23.23 

47.53 

23.44 

47.43 

23.65 

47.33 

23.88 

53 

54 

48.53 

23.87 

48.43 

23.88 

48.33 

24.09 

48 22 

24.31 

54 

55 

49.43 

24.11 

49.33 

24.33 

49.22 

24.54 

49.11 

24.76 

55 

56 

50.33 

24.55 

50.22 

24.77 

50.12 

24.99 

50.01 

25.21 

56 

57 

51.23 

24.99 

51.12 

25.21 

51.01 

25- 43 

50.90 

25.66 

57 

5S 

52.13 

25.43 

52.02 

25.65 

51.91 

25 S3 

51.79 

26.11 

53 

59 

53.03 

25.86 

52.92 

26.09 

52.80 

26.33 

52.69 

26.56 

59 

60 

53.93 

26.30 

53.81 

26.54 

53.70 

26 77 

53.58 

27.01 

60 

61 

64.83 

26.74 

54.71 

26.98 

54.59 

27.22 

54.47 

27.46 

61 

62 

55.73 

27.18 

55.61 

27.42 

55.49 

27.66 

55.36 

27.91 

62 

63 

56.62 

27.62 

56.50 

27.86 

56.38 

28.11 

56.26 

28.38 

63 

64 

57.52 

23.06 

57.40 

28.31 

57.23 

28.56 

57.15 

23.81 

64 

85 

58.42 

23.49 

58.30 

23.75 

58.17 

29.00 

58.0 4 

29.26 

65 

66 

59.32 

28.93 

59.19 

29.19 

59.07 

29.45 

58.94 

29.71 

66 

67 

60.22 

29.37 

60.09 

23.63 

59.96 

29.90 

59.83 

30. 16 

67 

63 

61.12 

29.81 

60.99 

39.08 

60.88 

30.34 

60.72 

30.61 

68 

69 

62.02 

30.25 

61.88 

30.52 

61.75 

30.79 

61.62 

31.08 

69 

70 

62.92 

30.69 

62.78 

30.96 

62.65 

31.23 

62.51 

31.51 

70 

71 

63.81 

31.12 

63.68 

31.40 

63.54 

31.08 

63.40 

31.96 

71 

72 

64.71 

31.56 

64.57 

31.84 

64.44 

32.13 

64.29 

32.41 

72 

73 

65.61 

32.00 

65.47 

32.29 

65.33 

32.57 

65.19 

32.86 

73 

74 

66.51 

32.44 

66.37 

32.73 

66.23 

33.02 

68.08 

33.3 1 

74 

75 

67.41 

32.88 

67.27 

33.1 7 

67.12 

33.46 

66.97 

33.76 

75 

75 

68.31 

33.32 

68.16 

33.61 

68.01 

33.91 

67.87 

34.21 

76 

77 

69.21 

33.75 

69.06 

34.06 

63.91 

34.36 

63.76 

31.66 

77 

78 

70.1! 

34.19 

69.96 

34.50 

69.80 

34.80 

69.65 

35.11 

78 

79 

71.00 

34.63 

70.85 

34.94 

70.70 

35.25 

70.55 

35.56 

79 

SO 

71.90 

35.07 

71.75 

35.33 

71 .59 

35.70 

71.44 

38.01 

80 

81 

72.80 

35.51 

72.65 

35.83 

72.49 

35.14 

72.33 

36.46 

81 

82 

73.70 

35.95 

73.54 

36.27 

73.38 

36.59 

73.22 

36.91 

82 

83 

7 1.60 

33.38 

71.44 

33.71 

74.28 

37.03 

1 74. 12 

37.36 

83 

84 

75.50 

36.82 

75.34 

37.15 

75.17 

37.48 

! 75.01 

37.81 

84 

85 

76.40 

37.26 

76. *3 

37.59 

76.07 

37.93 

75.90 

38.26 

85 I 

86 

77.30 

37.70 

77.13 

39.04 

76.96 

38.37 

78.80 

38.71 

88 | 

87 

78.20 

38.14 

78.03 

38 43 

77.86 

33.82 

77.00 

39. 16 

87 

88 

79.09 

38.58 

78.92 

38.92 

78.75 

39.27 

78.58 

39.61 

83 

89 

79.99 

39.0 i 

79.82 

30.36 ! 

79.65 

39.71 

79.48 

40.08 

89 | 

90 

•80.89 

39.45 

80.72 

39.81 1 

80.54 

40.16 

80.37 

40.51 

90 | 

91 

81.79 

39.89 

81.62 

10.25 ' 

81 .44 

40.60 

! 81.26 

40.93 

91 | 

92 

82.69 

40,33 

82.5 l 

40.69| 

82.33 

41.05 

! S2.15 

41.41 

92 8 

93 

S3.59 

40.77 

83.41 

41.13 

83.23 

41.50 ' 

83.05 

41.86 

93 

94 

81.49 

41.21 

!84.31 

41.58 ! 

84.12 

41.94 

;83.94 

42.31 

94 

95 

85.39 

41.65 1 

;85.20 

42.02 ! 

85.02 

42.39 

84.83 

42.76 

95 

96 

86.23 

42.03 

;86.10 

42.46 1 

85.91 

42.83 

85.73 

43.21 

88 1 

97 

H7. !8 

42.52 

87.00 

42.90 ; 

86.81 

43.28 

86.62 

43.60 

97 

98 

8.8.03 

42.96 

187.89 

4 3.31! 

87.70 

43.73 

87.51 

4 1.11 

98 

99 

83.98 

43.40 

88.79 

43.79j 

83.60 

44.17 

88.40 

41.53 

99 

100 

89.88 

43.84 

89.6 c 

44.23 

89.49 

44.62 1 

89.30 

45.01 

100 | 

§ 

d 

Dep. 

L n, t. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

i i 

g 

03 

3 

64 Deg. 

631 Deg. 

1 

63} 

stBWccsraaioH 

Deg. 

63} Deg. 

.2 

Cl 
































































































66 


TRAVERSE TABLE 


u 

27 Deg. 

27J Deg. 

27-j Deg. 

27 \ Deg. 

1 

•3 

tmJ • 

to 

r+ 

P 

S3 

O 

CD 

g 1 

p 

1 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

Lat 

Dep. 

■ ] 

0.89 ’ 

“05 

0.S9 

0.46 

0.89 

1.46 

CO 

0.47 

i 

o 

1 7^ j 

0.91 | 

1.78 

0.92 

1.77 

0.92 1 

1.Y7 

0.9 3 

2 

3 

2.07 

1.36 

2.67 

1.37 

2.66 

1.39 ! 

? 65 1 

i .40 

3 

4 

3.56 

1.82 

3.56 

1.83 

3.55 

1.85 |i 

3. i> 1 

1.86 

M 

5 ■ 

4.45 

2.27 

4.45 

2.29 

4.44 

2.31 ! 

4.42 

O QQ 

5 } 

6 

5.35 

2.72 

5.33 

2.75 

5.32 

2,77 1 

5.31 

2.79 1 

6 { 

7 

6.24 

3.18 

6.22 

3.21 

6.21 

3.23 

6.19 

3.26 

7 

8 

7 1 s 

3.63 

7.11 

3.66 | 

7.10 

3.69 | 

7.08 

3.72 

8 

o 1 

8.02 

4.09 

8.00 

4.12 ’ 

7.98 

4.16 

7.96 

4. 19 

9 

10 

8.91 

4.54 

8.89 

4.58 | 

8.87 

4.62 1 

8.85 

4.66 

10 

H 

9.80 

4.99 

9.78 

5.04 

9.76 

5.08 j 

9.73 

5.12 

11 

12 i 

10.69 

5.45 

10.67 

5.49 

10.64 

5.54 | 

10.62 

5.59 

12 

13 1 

11.58 

5.90 

11 .56 

5.95 

11.53 

6.00 | 

11.50 

6.05 

13 

14 | 

12.47j 

6.38 

12.45 

6.41 ; 

12.42 

6.46 l 

12.39 

6.52 

14 

15 ! 

13.37 

6.81 

13.34 

6.87 

13.31 

6.93 II 

13.27 

6.98 

15 

10 

14.20 

7.26 

14.22 

7.33 

14.19 

7.39 || 

14.16 

7.45 

16 

1/ i 

15.15 

7.72 

15.11 

7.78 

15.08 

7.85 , 

15.04 

7.92 

17 

18 

10.04! 

8.17' 

16.00 1 

8.24 1 

15.97 

8.31 J 

15.93 

8.38 

18 

19 

16.93 i 

8.63 1 

16.89 

8.70 ; 

16.85 

8.77 ! 

16.81 

b. 83 

19 

2-0 ! 

17.82 | 

9.08 | 

17.78 

9.16! 

17.74 

9.23 I 

17.70 

9.31 

20 

21 

18.71 

9.53 

j 18.67 

9.62 

18.63 

9.70 j 

18.58 

9.78 

21 

‘>9 

19.60 

9.99 

!19.56 

10.07 

19.51 

10.16 

19.47 

10.24 

22 

23 

90.49 

10.44 

| 20.45 

10.53 

20.40 

10.62 | 

20.35 

10.71 

23 

24 

21.38 

10.90 

i21.34 

10.99 

21.29 

11 .08 

21.24 

11 .17 

24 

25 

22.28 

11.35 

22.23 

11.45 

22.18 

11.54 

22.12 

1 1 .64 

25 

9n 

23. 1 7 

11.80 

23.11 

11.90 

23.06 

12.01 

23.01 

12.11 

26 

2 7 

24.06 

12.26 

24.00 

12.36 

23.95 

12.47 1 

23.89 

12.57 

27 

23 

24.95 

12.71 

24.89 

12.82 

24.84 

12.93 

1 24.78 

13.04 

28 

29 

25.84 

13.17 

25.78 

13.28 

25.72 

13.39 

|25.66 

13.50 

29 

30 

26.73 

13.62 

26.67 

13.74 

26.61 

13.85 

26.55 

13.97 

30 

31 

27.62 

14.07 

27.56 

14.19 

27.50 

14.31 

27.43 

14.43 

31 

32 

23.51 

14.53 

| 28.45 

14.65 

28.38 

14.78 

28.32 

l 14.90 

32 

33 

29.40 

14.98 

I! 29.34 

15.11 

29.27 

15.24 

!29.20 

| 15.37 

33 

34 

30.29 

15.44 

|| 30.23 

15.57 

30.16 

'5.70 

130.09 

115.83 

34 

35 

i 31 . 19 

15.89 

31.12 

16.03 

i31.05 

16.16 

130.97 

| 16.30 

35 

36 

32.08 

16.34 

| 32.00 

16.48 

31,93 

10.62 

| 1 ■.86 

16.76 

36 

37 

!32.97 

16.80 

j32.89 

16.94 

32.82 

; 17.08 

A l . 74 

17.23 

37 

38 

|33.86 

17.25 

33.78 

17.40 

,33.71 

17.55 

| 33.6*3 

17.69 

38 

39 

34.75 

17.71 

34.67 

17.86 

34.59 

18.01 

34.51 

18. Hi 

39 

40 

35.64 

18.16 

35.56 

18.31 

35.48 

18.47 

35.40 

18.62 

40 

41 

36.53 

18.61 

36.45 

18.77 

! 36.37 

18.93 

36.28 

19.09 

41 

42 

37.42 

!19.07 

37.34 

19.23 

;37.25 

1 19.39 

I 37.17 

19.56 

42 

43 

38.31 

19.52 

1 38.23 

19.69 

38.14 

| 19.86 

j 38.05 

20.02 

43 

44 

39.20 

1 19.98 

1 39.12 

20.15 

39.03 

20 : 32 

38.94 

20.49 

44 

45 

| 40.10 

20.43 

|40.01 

1 20 . 60 

39 . 92 

20.78 

39.82 

20.95 

45 

46 

40.99 

20 . 88 

140.89 

21.06 

40.80 

21 . 24 

40.71 

21.42 

i 46 

47 

41 .88 

21 . 34 

j 41.78 

21.52 

41.69 

1 21 . 70 

41.59 

21.83 

! 47 

48 

42.77 

| 21.79 

■ 42.67 

21.98 

11 42.58 

22.16 

42 .48 

22 . 35 

i 48 

49 

43.66 

22.25 

43.56 

22.44 

I 43.46 

22 . 63 

43.36 

1 22.82 

i 49 

50 

44.55 

22.70 

lj 44.45 

22.89 

44.35 

23. ID 

4V.25 

23 28 

| 50 

Distance. 

Dep. 

Lat. 

| D °l>* 

Lat. 

Dep. 

Lat 

Dep. 

Lat. 

t 

Distance.] 

63 Deg. 

62] Deg. 

62^ 

Z’.i ate. 

p 






























































































TRAVERSE TABLE. 


57 


o 

sr 

r*- 

P 

27 Deg. 

271 

Deg. 

971 

Deg. 

27J Deg. 

C 

Ul‘ 

a 

o 

CO 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

D 

O 

CO 

51 

45.44 

23.15 

45.34 

23.35 j 

45.24 

23.55 

45.13 

23.75 

“si 

62 

46.33 

23.61 

!46.23 

23.81 ! 

48.12 

24,01 

46.02 

24.21 

CO 

; 53 

47.22 

24.06 

1 47.12 

24.27j 

47.01 

24.47 

46.90 

24.68 

53 

54 

4S.il 

24.52 

48.01 

24.73 

47.90 

24.93 

47.79 

25.14 

545 

' 65 

49.01 

24.97 

48.90 

25.18 

48.79 

25.40 

48.67 

25.61 

55 

5(5 

49.90 

25.42 

49.78 

25.64 

49.67 

25.86 

49.56 

26.07 

56 

57 

50.79 

25.88 

50.67 

26.10 

50.53 

26.32 

50.44 

26.54 

57 

58 

51.68 

26.33 

51.56 

26.56 

51 o45 

26.78 

51.33 

27.01 

58 

59 

52.57 

26.79 

52.45 

27.01 

52.33 

27.24 

52.21 

27.47 

59 

60 

53.46 

27.24 

53.34 

27.47 

53.22 

27.70 

53.10 

27.94 

60 

61 

54.35 

27.69 

54.23 

27 .93 

54.11 

28.17 

53.98 

28.40 

61 

62 

55.24 

28.15 

55.12 

28.39 

54.99 

28.63 

54.87 

28.87 

29.33 

62 

63 

58.13 

28.60 

56.01 

28.85 

55.88 

29.09 

55.75 

63 

64 

57.02 

29.06 

56.90 

29.30 

56.77 

29.55 

58.64 

29.80 

64 

65 

57 92 

29.51 

57.79 

29.76 

57.66 

30.01 

57.52 

30.26 

65 

66 

58.81 

29.96 

58.68 

30.22 

58.54 

30.48 

58.41 

30.73 

66 

67 

59.70 

30.42 

59.56 

30.68 

59.43 

30.94 

59.29 

31.20 

67 

68 

60.59 

30.87 

60.45 

31.14 

60.32 

31 .40 

60.18 

31.66 

68 

69 

61.43 

31.33 

61.34 

31 .59 

61.20 

31 .86 

61.08 

32.13 

69 

70 

62.37 

31.78 

62.23 

32.05 

62.09 

32.32 

61.95 

32.59 

70 

71 

63.26 

32.23 

63,12 

32.51 

62.98 

32.78 

62.83 

33.06 

71 

712 

64.15 

32.69 

64.01 

32.97 

63.86 

33.25 

63.72 

33.52 

72 

73 

65.04 

33.14 

64.90 

33.42 

64.75 

33.71 

64.60 

33.99 

73 

74 

65.93 

33.60 

65.79 

33.88 

65.64 

34.17 

65.49 

34.46 

74 

' 75 

66.83 

34.05 

66.68 

34.34 

66.53 

34.63 

66.37 

34.92 

75 

76 

67.72 

34.50 

67.57 

34.80 

67.41 

35.09 

67.26 

35.39 

76 

77 

68.61 

34.96 

63.45 

35.26 

68.30 

35.55 

68.14 

35.85 

77 

78 

69.50 

35.41 

69.34 

35.71 

69.19 

36.02 

69.03 

36.32 

78 

79 

70.39 

35.87 

70.23 

36.17 

70.07 

36.48 

69.91 

36.73 

79 

80 

71.28 

36.32 

7M2 

36.63 

70.96 

36.94 

70.80 

37.25 

80 

81 

72.17 

36.77 

72.01 

37.00 

71.85 

37.40 

71.68 

37.71 

81 

82 

73.06 

37.23 

72.90 

37.55 

72.73 

37.88 

72.57 

38.18 

82 

83 

73.95 

37.68 

73.79 

38.00 

73.62 

33.33 

73.45 

38.65 

83 

84 

74.84 

38.14 

74.68 

38.48 

74.51 

38.79 

74.34 

39.11 

84 

85 

75.74 

3S.59 

75.57 

38.92 

75.40 

39.25 

75.22 

39.58 

85 

86 

76.63 

39.04 

76.46 

39.38 

76.28 

39.71 

76.11 

40.04 

86 

87 

77.52 

39.50 

77.34 

39.83 

77.17 

40.17 

76.99 

40.51 

87 

88 i 

78.41 

39.95 

78.23 

40.29 

78.06 

40.63 

77.88 

40.97 

88 

89 

79.30 

40.41 

79.12 

40.75 

78.94 

41.10 

78.76 

41.44 

89 

90 

80.19 

40.86 

8-0.01 

41.21 

79.83 

41.56 

79.65 

41.91 

90 

91 1 

81.08 ! 

41.31 

80.90 

41.67 

80.72 

42.02 

80.53 

42.37 

91 

! 92 

81 971 

41.77 

81.79 

42.12 

81.60 

42.4S 

81.42 

42.84 

92 

93 1 

82.86 I 

42.22 

82.68 

42.58 

S2.49 

42.94 

82.30 

43.30 

93 

94 1 

83.75 

42.68 

83.57 

43.04 

83.33 

43.40 

83.19 

43.77 

94 

95 | 

84.65 

43.13 

84.46 

43.50 

84.27 

43.87 

84.07 

44.23 

95 

96 j 

85,54 

43.58 

85.35 

43.96 

85.15 

44.33 

84.96 

44.70 

96 

97 

86.43 

44.04 

86.23 

44.41 

86.04 

44.79 

85.84 

45.10 

97 

98 ! 

87.32 

44.49 

87.12 

44.87 

86.93 

45.25 

86.73 

45.63 

98 


88.21 

44.95 

88.01 

45.33 

87.81 

45.71 

87.61 

46.10 

99 

100 1 

89.10 

45.40 

88.90 

45.79 

88.70 

46.17 

88.50 

46.56 

100 

2 1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

Lat. i 

Dep. 

Lat. 

i 

Distance.| 

1 

as 

| 

r 

63 .Deg. 

62} Deg. 

62k Deg. 

62; Deg. 

1 





















































































































58 


TRAVERSE TABLE 




o 
►— • 

OQ 

<r** 

23 Deg. 

28} Deg. 

23i 

Deg. 

28.| Deg. 

J 

i 

r— 

p 

3 

o 

a 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lett* 

Dep. 

3 

a 

a 

1 

0.88 

0.47 

0.88 

0.47 

0.88 

0.48 

0.88 

0.48 

1 

2 

1.77 

0.94 

1.76 

0.95 

1.76 

0.95 

1.75 

0.96 

2 

3 

2.65 

1.41 

2.64 

1.42 

2.64 

1.43 

2.63 

1.44 

3 

4 

3.53 

1.88 

3.52 

1.89 

3.52 

1.91 

3.51 

1.92 

4 

5 

4.41 

2.35 

4.40 

2.37 

4.39 

2.39 

4.38 

2.40 

5 

G 

5.30 

2.82 

5.29 

2,84 

5.27 

2.86 

5.26 

2.89 

6 

7 

6.18 

3.29 

6.17 

3.31 

6.15 

3.34 

6.14 

3.37 

7 

8 

7.06 

3.76 

7.05 

3.79 

7.03 

3.82 

7.01 

3.85 

8 

9 

7.95 

4.23 

7.93 

4.26 

7.91 

4.29 

7.89 

4.33 

9 

10 

8.83 

4.69 

8 .SI 

4.73 

8.79 

4.77 

8.77 

4.81 

10 

11 

9.71 

5.16 

9.69 

5.21 

9.67 

5.25 

9.64 

5.29 

11 

12 

10.60 

5.63 

10.57 

5.68 

10.55 

5.73 

10.52 

5.77 

12 

13 

11.48 

6.10 

11.45 

6.15 

11.42 

6.20 

11.40 

6.25 

13 

14 

12.36 

6.57 

12.33 

6.63 

12.30 

6.68 

12.27 

6.73 

14 

15 

13.24 

7.04 

13.21 

7.10 

13.18 

7.16 

13.15 

7.21 

15 

16 

14.13 

7.51 

14.09 

7.57 

14.06 

7.63 

14.03 

7.70 

16 

17 

15.01 

7.98 

14.98 

8.05 

14.94 

8.11 

14.90 

8.18 

17 

18 

15.89 

8.45 

15.86 

. 8.52 

15.82 

8.59 

15.78 

8.66 

18 

19 

16.78 

8.92 

16.74 

8.99 

16.70 

9.07 

16.66 

9.14 

19 

20 

17.66 

9.39 

17.62 

9.47 

17.58 

9.54 | 

17.53 

9.62 

20 

21 

18.54 

9.86 

18.50 

9.94 

18.46 

10.02 

18.41 

10.10 

21 

22 

19.42 

10.33 

19.38 

10.41 

19.33 

10.50 

19.29 

10.58, 

22 

23 

20.31 

10.80 

20.26 

10.89 

20.21 

10.97 

20.16 

11.06 

23 

24 

21.19 

11.27 

21.14 

11.36 

21.09 

11.45 

21.04 

11.54 

24 

25 

22.07 

11.74 

22.02 

11.83 

21.97 

11.93 

21.92 

12.02 

25 

2G 

22.96 

12.21 

22.90 

12.31 

22.85 

12k4l 

22.79 

12.51 

26 

27 

23.84 

12.68 

23.78 

12.78 

23.73 

12.88 

23.67 

12.99 

27 

28 

24.72 

13.15 

24.66 

13.25 

24.61 

13.36 

24.55 

13.47 

28 

29 

25.61 

13.61 

25.55 

13.73 

25.49 

13.84 1 

25.43 

13.95 

29 

30 

26.49 

14.08 

26.43 

14.20 

26.36 

14.31 

26.30 

14.43 

30 

31 

27.37 

14.55 

27.31 

14.67 

27.24 

14.79 

27.18 

14.91 

31 

32 

28.25 

15.02 

28.19 

15.15 

28.12 

15.27 

28.06 

15.39 

32 

33 

29.14 

15.49 

29.07 

15.62 

29.00 

15.75 ) 

28.93 

15.87 

33 

34 

30.02 

15.96 

29.95 

16.09 

29.88 

16.22 

29.81 

16.35 

34 

35 

30.90 

16.43 

30.83 

16.57 

!30.76 

16.70 

30.69 

16.83 

35 

36 

31.79 

16.90 

31.71 

17.04 

31.64 

17.18 

31.56 

17.32 

36 

37 

32.67 

17.37 

32.59 

17.51 

32.52 

17.65 

32.44 

17.80 

37 

38 

33.55 

17.84 

33.47 

17.99 

33.39 

18. 13 

i33.32 

18.28 

38 

39 

34.43 

18.31 

34.35 

18.46 

34.27 

18.61 

!34.19 

18.76 

39 

40 

35.32 

18.78 

35.24 

18.93 

35.15 

19.09 

j35.07 

19.24 

40 

41 

36.20 

19.25 

36.12 

19.41 

36.03 

19.56 

35.95 

19.72 

41 

42 

37.08 

19.72 

37.0 0 

19.88 

36.91 

20.04 

36.82 

20.20 

42 

43 

37.97 

20.19 

37.88 

20.35 

37.79 

20.52 

!37.70 

20.68 

43 

44 

38.85 

20.66 

38.76 

20.83 

38.67 

20.99 

38.58 

21.16 

44 

45 

39.73 

21.13 

39.64 

21.30 

39.55 

21.47 

139.45 

21.64 

45 

4G 

40.62 

21.60 

!40.52 

21.77 

40.43 

21.95 

140.33 

22.13 

46 

47 

41.50 

22.07 

141.40 

22.25 

41.30 

22.43 

i41.21 

22.61 

47 

48 

42.38 

22.53 

42.28 

22.72 

42.18 

22.90 

j42.08 

23.09 

48 

49 

43.26 

23.00 

43.16 

23.19 

43.06 

23.38 

42.96 

23.57 

49 

50 

44.15 

23.47 

44.04 

23.67 

43.94 

23.86 

43.84 

24.05 

50 

© 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

Dep. 

j Lat. 

6 

o 

c 

c3 

W 

CD 

P 

62 Deg. 

6 If Deg. 

’1 

6 H- 

Deg. 

61} Deg. 

ri 

c n 

5 










































































































50 


TRAVERSE TABLE. 


c 

«—►• ! 

28 Deg. 

28\ Deg. 

28% Deg. 

28f Deg. 

o 

w * 

r** 

a 

a 

(B 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. | 

Dep. 

Lat. 

Dep. 

3 

O 

a 

51 

45.03 

23.94 

44.93 

24.14 

•14.82 I 

24.34 

44.71 

24.53 

51 

■ 52 

45.91 

24.41 

45.81 | 

24.61 

45.70 

24.81 

45.59 

25.01 

52 

53 46.80 

24.88 

46.69 | 

25.09 

46.58 

25.29 

46.47 

25.49 

53 

54 

47.68 

25.35 

47.57 

25.56 

47.46 

25.77 

47.34 

25.97 

54 

55 ;48.56 

25.82 

48.45 

26.03 

48.33 

26.24 

48.22 

26.45 

55 

56 

49.45 

26.29 

49.33 

26.51 

49.21 

26.72 

49.10 

26.94 

56 

57 

50.33 

26.76 

50.21 

26.98 

50.09 

27.20 

49.97 

27.42 

57 

58 

51.21 

27.23 

51.09 

27.45 I 

50.97j 

27.68 

50.85 

27.90 

58 

59 

52.09 

27.70 

51.97 

27.93! 

51.85 : 

28.15 

51.73 

28.38 

59 

60 

52.98 

28.17 

52.85 

28.40 | 

52.73 

28.63 

52.60 

28.86 ! 

60 

61 

53.86 

28.64 
29.11 

53.73 

28.87 

53.61 

29.11 

53.48 

29.34 

61 

62 

54.74 

54.62 

29.35 

54.40 

29.58 | 

54.36 

29.82 

62 

63 

55.63 

29.58 

55.50 

29.82 

55.37 

30.06 

55.23 

30.30 

63 

64 

56.51 

30.05 

56.38 

30.29 

56.24 

30.54 

58.11 

30.78 

64 

65 

57.39 

30.52 

57.26 

30.77 

57.12 

31.02 

56.99 

31.26 

65 

66 

58.27 

30.99 

58.14 

31.24 ! 

:58.00 

31.49 

57.86 

31.75 

66 

67 

59.10 

31.45 

59.02 

31.71 

j 58.88 

31.97 

58.74 

32.23 

67 

68 

60.04 

31.92 

59.90 

32.19 

t 59.76 

32.45 

59.62 

32.71 

68 

69 

60.92 

32.39 

60.78 

32.66 

60.64 

32.92 

60.49 

33.19 

69 

70 

61.81 

32.86 

61.66 

33.13 

61.52 

33.40 

61.37 

33.67 

70 

71 

62.69 

33.33 

62.54 

33.61 

I 62.40 

33.88 

62.25 

34.15 

71 

72 

63.57 

33.80 

63.42 

34.08 

! 63.27 

34.36 

63.12 

34.63 

72 

73 

64.46 

34.27 

1 64.30 

34.55 

64.15 

34.83 

64.00 

35.11 

73 

74 

65.34 

34.74 

! 65.19 

35.03 

65.03 

35.31 

!64.88 

35.59 

74 

75 

66.22 

35.21 

! 66.07 

35.50 

65.91 

35.79 

i65.75 

36.07 

75 

76 

67.10 

35.68 

66.95 

35.97 

66.79 

36.26 

|66.63 

36.56 

76 

77 

67.99 

36.15 

67.83 

36.45 

67.67 

36.74 

67.51 

37.04 

77 

78 

68.87 

36.62 

68.71 

36.92 

68.55 

37.22 

68.38 

37.52 

78 

79 

69.75 

37.09 

69.59 

37.39 

69.43 

37.70 

j 69.26 

38.00 

79 

80 

70.64 

37.56 

70.47 

37.87 

70.31 

38.17 

70.14 

38.48 

80 

81 

71.52 

38.03 

71.35 

38.34 

71. IS 

38.65 

71.01 

38.96 

81 

82 

72.40 

38.50 

72.23 

38.81 

72.06 

39.13 

71.89 

39.44 

82 

83 

73.28 

38.97 

73.11 

39.29 

72.94 

39.60 

72.77 

39.92 

83 

84 

74.17 

39.44 

73.99 

39.76 

73.82 

40.08 

73.64 

40.40 

84 

85 

75.05 

30.91 

74.88 

40.23 

74.70 

40.56 

74.52 

40.88 

85 

86 

75.93 

40.37 

75.76 

40.71 

75 58 

41.04 

75.40 

41.36 

86 

87 

76.82 

40.84 

76.64 

41.18 

76.46 

41.51 

76.23 

41.85 

87 

88 

77.70 

41.31 

77.52 

41.65 

77.34 

41.99 

77.15 

42.33 

88 

89 

78.58 

41.78 

78.40 

42.13 

78.21 

42.47 

78.03 

42.81 

89 

90 

79.47 

42.25 

79.28 

42.60 

79.09 

42.94 

78.91 

43.29 

90 

91 

80.35 

42.72 

80.16 

43.07 

79.97 

43.42 

79.78 

43.77 

91 

92 

81.23 

43.19 

81.04 

43.55 

80.85 

43.90 

80.66 

44.25 

92 

93 

82.11 

43.66 

81.92 

44.02 

81.73 

44.38 

81.54 

44.73 

93 

94 

83.09 

44.13 

82.80 

44.49 

82.61 

44.85 

82.41 

45.21 

94 

95 

83.88 

44.60 

83.68 

44.97 

83.49 

45.33 

83.29 

45.69 

95 

96 

84.76 

45.07 

84.57 

45.44 

84.37 

45.81 

84.17 

46.17 

96 

97 

85.65 

45.54 

85.45 

45.91 

85.25 

46.28 

85.04 

46.66 

97 

98 

80.53 

46.01 

86.33 

46.39 

86.12 

46.76 

|85.92 

47.14 

98 

99 

87.41 

46.48 

87.21 

46.86 

87.00 

47.24 

86.80 

47.62 

99 

100 

88.29 

46.95 

88.09 

47.33 

87.83 

47.72 

|87.67 

48.10 

100 

a! 

o 

a 

Dep. 

Lat. 

Dep. 

Lat. 

Dep, 

Lat. 

Dep. 

Lat. 

© 

o 

c 

.2 

Cl 

62 Deg. 

6 If Deg. 

6 U Deg. 

613 Deg. 

d 

Tc 

• *>H 

P 






1 




i 














































































































60 


TRAVERSE TAELE 


Distance. 

1 

29 Deg. 

29} Deg. 

29 h Deg. 

29f Deg. 

Distance.! 

Lat • 

Dcp. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.87 

0.48 

0.87 

0.49 

0.87 

0.49 

0.87 

0.50 

1 

f 2 1 

1.75 

0.97 

1.74 

0.98 

1.74 

0.98 

1.74 

0.99 

2 

3 

2.62 

1.45 

2.62 

1.47 

2.61 

1.48 

2 .CO 

1.49 

3 

1 4 

3.50 

1.94 

3.49 

1.95 

3.48 

1.97 

3.47 

1.98 

4 

5 

4. 37 

2.42 | 

4.36 

2.44 

4.35 

2.46 

4.34 

2.48 

5 

6 

5.25 

2.91 1 

5.23 

2.93 

5.22 

2.95 

5.21 

2.98 

6 

7 

6.12 

3.39 i 

6.11 

3.42 

6.09 

3.45 

6.08 

3.47 

7 

8 

7.00 

3.SB 

G. 98 

3.91 

6.96 

3.94 

6.95 

3.97 

8 

9 

7.87 

4.36 

7.85 

4.40 

7.83 

4.43 

7.81 

4.47 

9 

10 

8 .75 ; 

4.85 ! 

8.72 

4.89 

8.70 

4,92 

8.68 

4.96 

10 

if 

9.62 I 

5.33 

9.60 

5.37 

9.57 

5.42 

9.55 

5.46 

11 

L2 

10.50 

5.82 ! 

10.47 

5.85 

10.44 

5.91 

10.42 

5.95 

12 

13 

11.37 

6.30 

11.34 

6.35 

11.31 

6.40 

11.29 

6.45 

13 3 

j 14 

12.24 

6 .79 1 

12.21 

6.84 

12.18 

6.89 1 

12.15 

6 .95 

14 

! 15 

13.12 

7.27 

13.09 

7.33 

13.06 

7.39 1 

13.02 

7.44 

15 

in 

13.99 

7.76 I 

13.96 

7.82 

13.93 

7.88 

13.89 j 

7.94 

16 

17 

14.87 

8.24 i 

14.83 

8.31 

14. SO 

8.37 

14.76 ! 

8.44 

17 

18 

15.74 

8.73 

15.70 

8.80 

15.67 

8.86 ! 

15.63 

8.93 

18 

19 

16.62 

9.21 

16.58 

9.28 

16.54 

9 .‘36 

16.50 | 

9.43 ! 

19 

20 

17.49 

9.70 

17.45 

9.77 

17.41 

9.85 

17.36 | 

9.92 

20 

21 

18.37 

10.18 

18.32 

10.26 

18.23 

10.34 I 

18.23 

10.42 ' 

21 

22 

19.24 

10.67 

19.19 

10.75 

19.15 

10.83 

19.10 

10.92 

22 3 

23 

20.12 

11.15 

20.07 

11.24 

20.02 

11.33 

19.97 

11 .41 

23 

24 

20.99 

11.64 

20.94 

11.73 

20.89 

11.82 1 

20.84 

11.91 

24 

^ 25 

21.87 

12.12 

21.81 

12.22 

21.76 

12.31 

21.70 

12.41 

25 

\ 2G 

22.74 

12.60 

22.68 

12*. 70 

22.63 

12.80 

22.57 

12.90 

26 

27 

23.61 

13.09 

23.56 

13.19 

1 23.50 

13.30 

23.44 

13.40 

27 

28 

24.49 

13.57 

24.43 

13.68 

24.37 

18.79 

24.31 

13.89 

28 

29 

25.36 

14.06 

25.30 

14.17 

25.24 

14.28 

!25.18 

14.39 

29 

30 

26.24 

14.54 

26.17 

14.06 

26.11 

14.77 

26.05 

14.89 

30 

31 

27.11 

15.03 

27.05 

15.15 

26.98 

15.27 

26.91 

15.38 

31 

32 

27.99 

15.51 

27.92 

15.64 

!27.85 

15.76 

27.78 

15.88 

32 

33 

28.86 

16.00 

28.79 

16.12 

| 28.72 

16.25 

! 28.65 

16.38 

33 

34 

29.74 

16.48 

29.66 

16.61 

]29.59 

16. n 

29.52 

16.87 

! 34 

35 

30.61 

16.97 

30.54 

17.10 

30.46 

17.23 

30.39 

17.37 

35 

36 

31.49 

17.45 

31.41 

17.59 

31.33 

17.73 

31.26 

17.86 

36 

37 

32.36 

17.94 

32.28 

18.08 

32.20 

18.22 

32.12 

18.36 

37 

38 

33.24 

18.42 

33.15 

18.57 

33.07 

18.71 

32.99 

18.86 

38 

39 

34.11 

18.91 

34.03 

19.06 

33.94 

19.20 

33.86 

19.35 

39 

40 

34.98 

19.39 

34.90 

19.54 

34.81 

19.70 

34.73 

|19.85 

40 

41 

35.86 

19.88 

35.77 

20.03 

35.68 

20.19 

35.60 

20.34 

41 j 

42 

36.73 

20.36 

36.64 

20.52 

36.55 

20.68 

|36.46 

20.84 

42 

43 

37.61 

20.85 

37.52 

21.01 

37.43 

21.17 

37.33 

21.34 

' 43 f 

44 

38.48 

21.33 

38.39 

21.50 

38.30 

21.67 

38.20 

21.83 

441 

45 

39.35 

21.82 

39.26 

21.99 

39.17 

22.16 

39.07 

22.33 

45 

46 

40.23 

j 22.30 

40.13 

22.48 

40.04 

22.65 

39.94 

22.83 

46 

47 

41.11 

22.79 

41.01 

9° 07 

40.91 

23.14 

40.81 

23.32 

47 i 

48 

41.9S 

OQ 97 

» A* » 

41.88 

23.45 

41.78 

23.63 

41.67 

23.82 

; 4SI 

49 

42.86 

23.70 

42.75 

23.94 

42.65 

24.13 

42.54 

24.31 

49 

50 

|43.73 

24.24 

43.62 

24.43 

43.52 

24.62 

43.41 

24.81 

50 

© 

o 

a 

c0 

*#■*> 

cn 

c 

j Dep. 

j Lat. 

Dep. 

Lat. 

Dpp. 

Lat. 

Dep. 

t Lat. 

| 6 

O 

1 C 

F 

l 61 

i 

Deg. 

601 Deg. 

60 } 

Deg. 

60} Deg. 

1 

c.a 




















































































































TB.VV1.HSK T.\ lifAi 


3 ) 


w* 

H* 

to 

r~+ 

P 

1 

l 29 Deg. 

29i Deg. 

29* 

Deg. 

291 Deg. 

**mm*itp 

O 

to 

& 

o 

p 

Lat. ' 

Dep. 

Ldt* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

P 

O 

p 

51 

44.61 

24.73 

44.50 

24.92 

44.39 

25.11 

44.28 

"25.31 

~51 

52 

45.48 

25.21 

45.37 

25.41 

45.26 

25.61 

45.15 

25.80 

52 

53 

46.35 

25.69 

46.24 

25.90 

46.13 

26.10 

46.01 

26.30 

53 

r>4 

47.23 

26.18 

47.11 

26.39 

47.00 

26.59 

46.88 

26.80 

54 

55 

48.10 

26.66 1 

47.99 

26.87 

47.87 

27.08 

47.75 

27.29 

55 

56 

48.98 

27.15 j 

48.86 

27.36 

48.74 

27.58 

48.62 

27.79 

56 

57 

49 .85 

27.63 

49.73 

27.85 

49.61 

28.07 

49.49 

28.28 

57 

53 

50,73 

28.12 

50.60 

28.34 

50.48 

28.56 

50.36 

28.78 

58 

59 

51.60 

28.60 

51.48 

28.83 

51.35 

29.05 

51.22 

29.28 

59 

60 

52.48 

29.09 

52.35 

29.32 

52.22 

29.55 

52.09 

29.77 

60 

61 

53.35 

29.57 

53.22 

29.81 

53.09 

30.04 

52.96 

30.27 

61 

62 

54.23 

30.06 

54.09 

30.29 

53.96 

30.53 

53.83 

30.77 

62 

63 

55.10 

30.54 

54.97 

30.78 

54.83 

31.02 

54.70 

31.26 

63 

64 

55 . 98 

31.03 

55.84 

31.27 

55.70 

31.52 

55 . 56 

31.76 

64 

65 

56.85 

31.51 

56.71 

31.76 

56.57 

32.01 

56.43 

32 . 25 

65 

66 

57.72 

32.00 

57.58 

32 . 25 

57,44 

32.50 

57.30 

32 . 75 

66 

67 

58.60 

32.48 ! 

58.40 

32.74 

58.31 

32.99 

58.17 

33 . 25 

67 8 

68 

59.47 

32.97 

59 . 33 

33.23 

59 . 18 

33.48 

59.04 

33.74 

68 

69 

60.35 

33.45 

60.20 

33.71 

60.05 

33.98 

59.91 

34.24 

69 1 

70 

61.22 

33.94 

61.07 

34.20 

60.92 

34.47 

60.77 

34.74 

70 j 

71 

62. 10 

34.42 | 

61.95 

34.69 

61.80 

34.96 

61.64 

35.23 

71 

72 

62.97 

34.91 

62.82 

35.18 

62.67 

35.45 

62.51 

35.73 

72 

73 

63.85 

35.39 

63.69 

35.67 

63.54 

35.95 

63.38 

36.22 

73 

74 

64.72 

35.88 

64.56 

36.16 

64.41 

30.44 

64.25 

36.72 

74 

75 

65.60 

36.36 

65.44 

36.65 

65.28 

36.93 

65.11 

37.22 

75 1 

76 

66.47 

36.85 

66.31 

37.14 

66.15 

37.42 

65.98 

37.71 

76 

77 

67.35 

37.33 

67.18 

37.62 

67.02 

37.92 

66.85 

38.21 

77 | 

78 

68.22 

37.82 

68.05 

38.11 

67.89 

38.41 

67.72 

38.70 

78 

79 

69.09 

38.30 

68.93 

38.60 

68.76 

38.90 

68 .59 

39.20 

79 

80 

69.97 

38.78 

69.80 

39.09 

69.63 

39.39 

69.46 

39.79 

80 

81 

70.84 

39.27 

70.67 

39.58 

70.50 

39.89 

70.32 

40.19 

81 

82 

71.72 

39.75 

71.54 

40.07 

71.37 

40.38 

71.19 

40.69 

82 

83 

72.59 

40.24 

72.42 

40.56 

72.24 

40.87 

72.06 

41.19 

83 

84 

73.47 

40.72 

73.29 

41.04 

73.11 

41.36 

72.93 

41.68 

84 

85 

74.34 

41.21 

74.16 

41.53 

73.98 

41.86 

73.80 

42.18 

85 

86 

75.22 

41.69 

75.03 

42.02 

74.85 

42.35 

74.67 

42.67 

86 

87 

76,09 

42.18 

75.91 

42.51 

75.72 

42.84 

75.53 

43.17 

87 

1 88 

76:97 

42.65 

76.78 

43.00 

76.59 

43.33 

76.40 

43.67 

88 

1 89 

77.84 

43.15 

77.65 

43.49 

77.46 

43.83 

77.27 

44.16 

89 | 

90 

78.72 

43.63 

78.52 

43.98 

78.33 

44.32 

78.14 

44.66 

90 | 

I 91 

79.59 

44.12 

79.40 

44.46 

79.20 

44.81 

79.01 

45.16 

91 I 

1 92 

80.46 

44.60 

80.27 

44.95 

80.07 

45.30 

79.87 

45.65 

921 

93 

81.34 

45.09 

81.14 

45.44 

SO. 94 

45.80 

80.74 

46.15 

93 \ 

f 94 

82.21 

45.57 

82.01 

45.93 

81.SI 

46.29 

81.61 

46.64 

94 

95 

83.09 

46.06 

82.89 

46.42 

82.68 

46.78 

82.48 

47.14 

1 95 

96 

83.96 

46.54 

83.76 

46.91 

83.55 

47.27 

83.35 

47.64 

96 

97 

84.84 

47.03 

84.63 

47.40 

84.42 

47.77 

84.22 

48.13 

! 97 

98 

85.71 

47.51 

85.50 

47.88 

85.29 

48.26 

85.08 

48.63 

i 98 

99 

86.59 

48.00 

86.38 

48.37 

86.17 

48.75 

85.95 

49.13 

99 

100 

87.46 

48.48 

87.25 

48.86 

87.04 

49.24 

86.82 

49.62 

1100 

<s 

•o 

a 

ci 

X 

Q 

Dep. 

Li CL t * 

Dep. 

Lat, 

Dep. 

Lat. 

Dep. 

Lat. 

a > 
o 

S3 

61 Beg. 

60 f Deg. 

60* 

Deg. 

60^ Deg. 

cd 

-*«> 

oa 

, * .-4 

! q 

1 


23 








































































































TRAVERSE TABLE. 


62 


Distance. 

30 Deg. 

30} Deg. 


Deg. 

30} Deg. 

■c 

£ 

o 

p 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0 . 

87 

0 . 

50 

0.86 

0.50 

0.86 

0.51 

0.86 

0.51 

I 

2 

1. 

73 

1. 

00 

1.73 

1.01 

1.72 

1.02 

1.72 

1.02 

2 

3 

2. 

60 

1. 

50 

2 59 

1.51 

2.58 1 

1.52 

2.58 

1.53 

3 

4 

3. 

46: 

2. 

00 

3.46 

2.02 

3.45 

2.03 

3.44 

2.05 

4 

5 

4 

33 

2. 

50 

4.32 

2.52 

4.31 

2.54 

4.30 

2.56 

5 

6 

5 

20 

3. 

00 

5.18 

?.02 

5.17 

3.05 

5.16 

3.07 

P 

7 

6 

06 

3. 

50 

6.05 

3.53 

0.03 

3.55 

6.02 

3.58 

i 

8 

6 

93 

4. 

00 

6.91 

4.03 

6.89 

4.06 

6.88 

4.09 

8 

9 

7 

79 

4. 

50 

7.77 

4.53 

7.75 

4.57 

7.73 

4.60 

9 

10 

8 

66 

5. 

00 

8.64 

5.04 

8.62 

5.08 

8.59 

5.11 

.0 

11 

9 

53 

5. 

50 

9.50 

5.54 

9.48 

5.58 

9.45 

5.62 1 

;] 

12 

10 

.39 

6. 

00 

10.37 

6.05 1 

10.34 

6.09 1 

10.31 1 

6.14 | 

12 

13 

11 

.26 

6. 

50 

11.23 

6.55 

11.20 

6.60 

11.17 

6.65 i 

13 

14 

12 

.12 

7. 

00 

12.09 

7.05 

12.06 

7.11 

12.03 

7. 16 

11 

15 

12 

.99 

7. 

50 

12.96 

7.56 | 

12.92 

7.61 : 

12. S9 

7.67 

15 

16 

13 

.86 

8. 

00 

13.82 

8.06 

13.79 

8.12 ! 

13.75 

8.18 

16 

17 

14 

.72 

8. 

50 

14.69 

8.56 

14.65 

8.63 i 

14.61 

8.69 

17 

18 

15 

.59 

9. 

00 

15.55 

9.07 

15.51 

3.14 

15.47 

9.20 

18 

19 

16 

.45 

9. 

50 

16.41 

9.57 

16.37 

9.64 

10.33 

9.71 

1!) 

20 

17 

.32 

10. 

00 

17.28 

10.08 

17.23 

10.15 | 

17.19 

10.23 

20 

21 

18 

. 19 

10 

50 | 

18.14- 

10.58 

18.09 

10. G6 

18.05 

10.74 

21 

22 

19 

05 

11. 

00 i 

19.00 

11.08 I 

18.96 

11.17 

18.91 

11.25 

22 

23 

19 

.92 

11 

50 

19.87 

11.59 | 

19.82 

11.67 

19.77 

11.76 

23 

24 

20 

.78 

12 

00 

20.73 

12.09 

20.68 

12.18 

20.63 

12.27 

24 

25 

21 

.65 

12 

50 

21.60 

12.59 

21.54 

12.69 

21 .49 

12.78 

25 

26 

22 

.52 

13 

00 

22.46 

13.10 

22.40 

13.20 ! 

22.34 

13.29 

26 

27 

23 

.33 

13 

50 

23.32 

13.60 

23.26 

13.70 I 

23.20 

13.80 

27 

28 

24 

.25 

14 

00 

24.19 

14.11 

24.13 

14.21 1 

24.06 

14.32 

28 

29 

25 

.11 

14 

50 

25.05 

14.61 

24.99 

14.72 

24.92 

11.83 

29 

30 

25 

. 9S 

15 

00 

25.92 

15.11 

25.85 

15.23 

25.78 

15.34 

30 

31 

26 

.85 

15 

50 

26.78 

15.62 

26.71 

15.73 

26.64 

15.85 

31 

32 

27 

.71 

16 

00 

27.64 

16.12 

27.57 

16.24 

27.50 

16.36 

32 

33 

28 

.58 

16 

50 

28.51 

16.62 

28.43 

16.75 

28.36 

16.87 

33 

34 

29 

.44 

17 

00 

29.37 

17.13 

29.30 

17.26 

29.22 

17.38 

34 

35 

30 

.31 

17 

50 

30.23 

•17.63 

30.16 

17.76 

!30.08 

17.90 

35 

36 

31 

. 18 

18 

00 

|31.10 

'18.14 

31.02 

18.27 

30.94 

18.41 

36 

37 

32 

.04 

18 

.50 

|3l.96 

18.64 

31.88 

18.78 

31.80 

18.92 

37 

38 

32 

.91 

19 

00 

i 32.83 

19.14 

32.74 

19.29 

32.60 

19 #43 

38 

39 

33 

.77 

19 

50 

| 33.69 

19.65 

33.60 

19.79 

33.52 

19.94 

39 

40 

34 

.64 

20 

.00 

34.55 

20.15 

34.47 

20.30 

34.38 

20.45 

40 

41 

35 

.51 

20 

.50 

35.42 

20.65 

35.33 

20.81 

35.24 

20.96 

41 

42 

36 

.37 

21 

.00 

{ 36.28 

21.16 

36.19 

| 21.32 

36.10 

21.47 

42 

43 

37 

.24 

21 

.50 

J 37.14 

21.66 

37.05 

21.82 

36.95 

21.99 

43 

44 

38 

.11 

22 

.00 

] 33.01 

22.17 

37.91 

22.33 

37.81 

22.50 

44 

45 

38 

.97 

22 

.50 

|38.87 

22.67 

38.77 

22.84 

38.67 ! 23.01 

15 

46 

39 

.84 

23 

.00 

I 39.74 

23.17 

39.63 

23.35 

39.53 

, 23.52 

4 c 

47 

1 40 

.70 

23 

.50 

!40.60 

23.68 

40.50 

23.85 

40.39 

! 24.03 

Vi 

48 

41 

.57 24 

.00 

41.46 

i24.18 

41.36 

24.36 

41.25 

24.54 

48 

49 

42 

.44 

24 

.50 

42.33 

24.68 

42.22 

24.87 

42.11 

25.05 

49 

50 

43 

.30 

25 

.00 

43.19 

25.19 

43.08 

25.38 

42.97 

25.56 

50 

j Distance. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c 

1 

60 Deg 

• 

59} Deg. 

59.’ Deg. 

59} Deg. 

ci 

+-> 

CG 

5 

. .... 
































































































































TRAVERSE TABLE. 


63 


e 

XJ1 

***** 

P 

O 

CD 

30 Deg. 

30} Deg. 

30^ Deg. 

30} Deg. 

i ^ 

! | 

1 I 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

— 

j Lat. 

Dep. 

51 

44.17 

25.50 

44.06 

25.69 

43.94 

25.88 

43.83 

26.08 

51 

5 2 

45.03 

26.00 

44.92 

28.20 

44.80 

26.39 

44.69 

26.59 

52 

53 

45.90 

26.50 

45.78 

26.70 

45.67 

26.90 

1 45.55 

27.10 

i 53 

54 

46.77 

27.00 

46.65 

27.20 

46.53 

27.41 

46.41 

27.61 

511 

55 

47.63 

27.50 

47.51 

27.71 

47.39 

27.91 

47.27 

28.12 

1 1 

i 55j 

56 

48.50 

28.00 

48.37 

28.2! 

48.25 

28.42 

48.13 

28.63 

1 561 

57 

49.36 

28.50 

49.24 

28.72 

149.11 

28 93 

48.99 

29.14 

! 57 

58 

50.23 

29.00 

50.10 

29.22 

|49.97 

29.44 

49.85 

29.65 

’ 58 

59 

51.10 

29.50 

50.97 

29.7 2 

50.84 

29.94 

50.70 

30.17 

59 

60 

51.96 

3U.00 

51.83 

30.23 

51.70 

30.45 

51 .56 

30.68 

60 

61 

52.83 

30.50 

52.69 

30.73 

i52.56 

30.96 

i52.42 

31.19 

’ 61 

62 

53.69 

31.00 

53.56 

31.23 

! 53.42 

31.47 

53.28 

31.70 

| 62 

63 

54.56 

31.50 

54.42 

31.74 

!54.28 

31.97 

54.14 

32.21 

i 83 

64 

55.43 

32.00 

55.29 

32.24 

155.14 

32.48 

55.00 

32.72 

! 64 

65 

56.29 

32.50 

56.15 

32.75 

58.01 

32.99 

55.86 

33.23 

65 

66 

57.16 

33.00 

57.01 

33.25 

!56.87 

33.50 

56.72 

33.75 

fi 6 

67 

58.02 

33.50 

57.88 

33.75 

57.73 

34.01 

57.58 

34.26 

| 67 

68 

58.89 

34.00 

58.74 

34.26 

58.59 

34.51 

58.44 

! 34.77 

i 68 

69 

59.76 

34.50 

59.60 

34.76 

59.45 

35.02 

59.30 

35.28 

69 

70 

60.62 

35.00 

60.47 

35.26 

60.31 

35.53 

60.16 

35.79 

; 70 

71 

61.49 

35.50 

61.33 

35.77 

161.18 

36.04 

61.02 

36.30 

i 71 

72 

62.35 

36.00 

62.20 

36.27 

62,04 

36.54 

i61.88 

36.81 

; 72 

73 

63.22 

36.50 

63.06 

36.78 

162.90 

37.05 

j 62.74 

37.32 

73 

74 

64.09 

37.00 

63.92 

37.28 

j 63.76 

37.56 

63.60 

37.84 

74 

75 

64.95 

37.50 

64.79 

37.78 

64.62 

38.07 

64.46 

38.35 

75 

76 

65.82 

38.00 

65.65 

38.29 

65.48 

38.57 

65.31 

38.86 

76 

77 

66.68 

38.50 

66.52 

38.79 

66.35 

39.08 

66.17 

39.37 

77 

78 

67.55 

39.00 

67.38 

39.29 

67.21 

39.59 

67.03 

39.88 

78 

79 

68.42 

39.50 

68.2-4 

39.80 

68.07 

40.10 

67.89 

40.39 

79 

80 

69.28 

40.00 

69.11 

40.30 

68.93 

40.60 

68.75 

40.90 

80 

81 

70.15 

40.50 

69.97 

40.81 

69.79 

41.11 

69.61 

41.41 

81 

82 

71.01 

41.00 

70.83 

41.31 

70.65 

41.62 

70.47 

41.93 

82 

83 

71.88 

41.50 

71.70 

41.81 

71.52 

42.13 

71.33 

42.44 

83 

84 

72.75 

42.00 

72.50 

42.32 

72.38 

42.63 

72.19 

42.95 

84 

85 

73.61 

42.50 

73.43 

42.82 

73.24 

43.14 

73.05 

43.46 

85 

86 

74.48 

43.00 

74.29 

43.32 

74.10 

43.65 

73.91 

43.97 

86 

87 

75.34 

43. #0 

75.15 

43.83 

74.96 

44.16 

74.77 

44.48 

87 

88 

76.21 

44.00 

76.02 

44.33. 

75.82 

44.66 

75.63 

44.99 

8 S 

89 

77.08 

44.50 

76.88 

44.84 , 

76.68 

45.17 

76.49 

45.51 

89 

90 

77.94 

45.00 

77.75 

45.34 

77.55 

45.68 

77.35 

46.02 

90 

91 

78.81 

45.50 

78.61 

45.84 

78.41 

46.19 

78.21 

46.53 

91 

92 

79.67 

46.00 

79.47 

48.35 

79.27 

46.69 

79.07 

47.04 

92 

93 

80.54 

46.50 

80.34 

46.85 

80.13 

47.20 

79.92 

47.55 

93 

94 

81.41 

47.00 

81.20 

47.35 

80.99 

47.71 

80.78 

48.06 

94 

95 

82.27 

47.50 

82.06 

47.86 

81.85 

48.22 

81.64 

48.57 

95 

96 

83.14 ! 

48.00 

82.93 

48.36 

82.72 

48.72 

82.50 

49.08 

96 

97 

84.00 

48.50 

83.79 

48.87 

83.58 

49.23 

83.36 

49.60 

97 

98 

84.87 

49.00 

84.66 

49.37 

84.44 

49.74 

84.22 

50.11 

98 

99 

85.74 

49.50 

85.52 

49.87 

85.30 

50.25 

85.08 

50.62 

29 

100 

86.60 

50.00 

86.38 ! 

50.38 

86.16 

50.75 

85.94 

51.13 

100 

• 

o 

o 

a 

Dep. 

! 

L cit. 

i 

Dep. | 

I-Jclt. 

Dep. 

L&t* 

Dep. 

Lat. 

g 

ci 

♦-> 

n 

i 

60 Deg. 

I 

59} Deg. 

69} Deg. 

59} Deg. 

c 



























































































































TRAVERSE TABLE. 


64 








I 




Distance. 

31 Deg. 

3U Deg. 

31 ^ Deg. 

3lf Deg. 

u 

Sc 

c* 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

? 

1 

0.86 

0.51 

0.85 

0.52 

0.85 

0.52 

0.85 

0.53 

i 

2 

1.71 

1.03 

1.71 

1.04 

1.71 

1.04 

1.70 

1.05 

2 

3 

2.57 

1.55 

2.56 

1.56 

2.56 

1.57 

2.55 

1.58 

3 

4 

3.43 

2.06 

3.42 

2.08 

3.41 

2.09 

3.40 

2.10 

4 

5 

4.29 

2.58 

4.27 

2.59 

4*. 26 

2.61 

4.25 

2.63 

5 

e 

5.14 

3.09 

5.13 

3.11 

5.12 

3.13 

5.10 

3.16 

6 

7 

6.00 

3.61 

5.98 

3.63 

5.97 

3.66 

6 .95 

3.68 

7 

8 

6.86 

4.12 

6.84 

4.15 

6.82 

4.18 

6.80 

4.21 

8 

9 

7.71 

4.64 

7.69 

4.67 

7.67 

4.70 

7.65 

4.74 

9 

10 

8.57 

5.15 

8.55 

5.19 

8.53 

5.22 

8.50 

5.26 

10 

11 

9.43 

5.67 

9.40 

5.71 

9.38 

5.75 

9.35 

5.79 

11 

12 

10 .29 

6.18 

10.26 

6.23 

10.23 

6.27 ! 

10.20 

6.31 

12 

13 

n . 14 

6.70 

11.11 

6.74 

11.08 

6.79 

11.05 

6.84 

13 

14 

12.00 

7.21 

11.97 

7.26 

11.94 

7.31 

11.90 

7.37 

14 

15 

12.86 

7.73 

12.82 

7.78 

12.79 

7.84 

12.76 

7.89 

15 

! 16 

13.71 

8.24 

13.68 

8.30 

13.64 

8.36 

13.61 

8.42 

16 

17 

14.57 

8.76 

14.53 

8.82 

14.49 

8.88 

14.46 

8.95 

17 

18 

15.43 

9.27 

15.39 

9.34 

15.35 

9.40 

15.31 

9.47 

18 

39 

16.29 

9.79 

16.24 

9.86 

16.20 

9.93 

16.16 

10.00 

19 

20 

17.14 

10.30 

17.10 

10.38 

17.05 

10.45 

17.01 

10.52 

20 

21 

18.00 

10.82 

17.95 

10*89 

17.91 

10.97 

1 17.86 

11.05 

21 

22 

18.86 

11.33 1 

18.8L 

11.41 

18.76 

11.49 1 

18.71 

11.58 

22 

23 

19.71 

11.85 

19.66 

11.93 

19.61 

12.02 

19.56 

12 . 10 

23 

24 

20.57 

12.36 ! 

20.52 

12.45 | 

20.46 

12.54 

20.41 

12.63 

24 

25 

21 .43 

12.88 

21.37 

12.97| 

21.32 

13.06 

21.26 

13.16 

25 

26 

22.29 

13.39 

22.23 

13.49 | 

22.17 

13.58 

,22.11 

13.68 

26 

27 

23.14 

13.91 

23.08 

14.01 

23.02 

14.11 

22.96 

14.21 

27 

28 

24.00 

14.42 1 

i23.94 

14.53 

23.87 

14.63 

23.81 

14.73 

28 

29 

24.86 

14.94 24.79 

15.04 

24.73 

15.15 

24.66 

15.26 

29 

30 

25.71 

15.45 | 25.65 

15.56 

25.58 

15.67 

|25.51 

15.79 

30 

31 

26.57 

15.97 

|26.50 

16.08 

26.43 

16.20 

i26.36 

16.31 

31 

32 

27.43 

16.48 

27.36 

16.60 

27.28 

16.72 

27.21 

16.84 

32 

33 

28.29 

17.00 

28.21 

17.12 

28.14 

17.24 

28.06 

17.37 

33 

34 

29.14 

17.51 

29.07 

17.64 

28.99 

17.76 

128.91 

17.89 

3*1 

35 

30.00 

18.03 

29.92 

18.16 

29.84 

18.29 

29.76 

18.42 

35 

36 

30.86 

18.54 

30.78 

18.68 

30.70 

18.81 

i30.61 

18.94 

36 

37 

31.72 

19.06 

31.63 

19.19 

31.55 

19.33 

31.46 

19.47 

37 

38 

32.57 

19.57 

32.49 

19.71 

32.40 

19.85 

32.31 

20.00 

38 

39 

33.43 

20.09 

33.34 

20.23 

33.25 

20.33 

33.16 

20 52 

39 

40 

34.29 

20.60 

34.20 

20.75 

34.11 

20.90 

34.01 

21 05 

40 

41 

35.14 

21.12 

35.05 

21.27 

34.96 

21.42 

34.86 

21.57 

41 

42 

36.00 

21.63 

35.91 

21.79 

35.81 

21.94 

35.71 

22.10 

42 

43 

36.86 

22.L5j 

36.76 

22.31 

36.66 

22.47 

36.57 

22.63 

43 

44 

37.72 

22.66 

37.62 

22.83 

37.52 

22.99 

37.42 

23.15 

44 

45 

38.57 

23.18 

138.47 

23.34 

38.37 

23.51 

38.27 

23.68 

45 

46 

39.43 

23.69 

39.33 

23.86 

39.22 

24.03 

39.12 

24.21 

46 

47 

'40.29 

24.21 

40.18 

24.38 

40.07 

24.56 

39.97 

24.73 

47 

48 

41.14 

24.72 

41.04 

24.90 

40.93 

25.08 

40.82 

25.26 

48 

49 

! 42.00 

25.24 

41.89 

25.42 

41.78 

25.60 

41.67 

25.78 

49 

50 

42.86 

25.75 

42.75 

25.94 

42.63 

26.12 

42.52 

26.31 

50 

d 

o 

c 

Dop. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

d 

d 

♦-> 

QO 

5 

59 Deg. 

58f Deg. 

58^ Deg. 

5S\ 0*cr. 

d 

r/3 

• 

i ~ 

t 

















































































































TRAVERSE TAELE 


65 


5 

Ul 

«-*• 

p 

31 

Deg. 

31^ Deg. 


314 

Deg. 

31£ Deg 


s 

W 

r* 

8 

o 

(t 

Lat. 

—r— ... 

Dep. 

Lat. 

! Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

2 

O 

? 

51 

i 43.72 

26.27 

43.60 

26 

.46 

43 

.48 

26 

.65 

43.37 

26 

84 

51 

52 

144.57 

26.78 

44.46 

26 

.98 

44 

.34 

27 

.17 

44.22 

27 

36 

52 

53 

45.43 

27.30 

45.31 

27 

.49 

45 

. 19 

27 

.69 

45.07 

27 

89 

53 

if 

46.29 

27.81 

46.17 

28 

.01 

46 

.04 

28 

.21 

45.92 

23. 

42 

54 

35 

47.14 

28.33 

47.02 

28 

«t)3 

46 

.90 

28 

.74 

46, 7 7 

1 28 

94 

55 

56 

48.00 

28.84 

47.88 

29 

.05 

47 

.75 

29 

. 26 

47.62 

29 

47 

56 

57 

48.86 

29.36 

48.73 

29 

.57 

48 

.60 

29 

.78 

48.47 

29 

99 

57 

58 

49.72 

29.87 

49.58 

30 

.09 

49 

.45 

30 

.30 

49.32 

30 

52 

53 

59 

50.57 

30.39 

50.44 

30 

.61 

50 

.31 

30 

.83 

50.17 

31. 

05 

59 

60 

51.43 

j 30.90 

51.29 

31 

.13 

51 

.16 

31 

.35 

w 51.02 

31 

57 

60 

|_~ 6 l 

52.29 

31.42 

52.15 

31 

. 65 

52 

.01 

31 

.87 

51.87 

32. 

10 

61 

62 

63.14 

31.93 

53.00 

32 

.16 

52 

.86 

32 

.39 

52.72 

32. 

63 

62 

63 

54.00 

32.45 

53.86 

32 

.68 

53 

.72 

32 

92 

53.57 

33. 

15 

63 

64 

54.86 

32.96 

54.71 

33 

.20 

54 

57 

33 

44 

54.42 

33. 

68 

64 

65 

55.72 

33.48 

55.57 

33 

.72 

55 

.42 

33 

96 

55.27 

34. 

20 

65 

66 

56.57 

33.99 

56.42 

34 

.24 

56 

.27 

34 

48 

56.12 

34. 

73 

66 

67 

57.43 

34.51 

57.28 

: 34 

.76 

57 

13 

35 

01 

56.98 

35. 

26 

67 

68 

58.29 

35.02 

58.13 

35 

.28 

57 

.98 

35 

53 

57.82 

35. 

78 

68 

69 

59.14 

35.54 

58.99 

35 

.80 

58 

.83 

36 

05 

58.67 

36. 

31 

69 

70 

60.00 

36.05 

59.84 

36 

31 

59 

68 

36. 

57 

59.52 

36. 

83 

70 

71 

60.86 

36.57 

60.70 

36 

83 

60 

"54 

37. 

10 

60.37 

37. 

36 

71 

72 

61.72 

37.08 

61.55 

37 

35 

61 

39 

37 

62 

61.23 

37. 

89 

72 

73 

62.57 

37.60 

62.41 

37 

87 

62 

24 

38. 

14 

62.08 

38. 

41 

73 

74 

63.43 

38.11 

63.26 

38 

39 

63 

10 

38. 

66 

62.93 

33. 

94 

74 

75 

64.29 

38.63 

64.12 

38. 

91 

63 

95 

39. 

19 

63.78 

39. 

47 

75 

76 

65.14 

39.14 

64.97 

39 

43 

64 

80 

39. 

71 

64.63 

39. 

99 

76 

77 

66.00 

39.66 

65.83 

39. 

95 1 

65 

65 

40. 

23 

65.48 

40. 

52 

77 

78 

66.80 

40.17 

66.68 

40. 

46 

66 . 

51 

40. 

75 

66.33 

41. 

04 

78 

79 

67.72 

40.69 

67.54 

40. 

98 

67. 

36 

41 

28 

67.18 

41. 

57 

79 

80 

68 .57 

41.20 

68.39 

41. 

50 

68 . 

21 

41 

80 

68.03 

42. 

10 

80 

81 

69.43 

41.72 

69.25 

42. 

02 

69. 

06 

42. 

32 

68.88 

42. 

62 

81 

82 

70.29 

42 . 2 a 

70.10 

42. 

54 

69. 

82 

42. 

84 

69.73 

43. 

15 

82 

83 

71.14 

42.75 

70.96 

43. 

06 

70. 

77 

43. 

37 

70.58 

43. 

68 

83 

84 

72.00 

43.26 

71.81 

43. 

58 

71. 

62 

43. 

89 

71.43 

44. 

20 

84 

85 

72.86 

43.78 

72.67 

44. 

10 

72. 

47 

44. 

41 

72.28 

44. 

73 

85 

86 

73.72 

44.29 

73.52 

44. 

61 

73. 

33 

44. 

93 

73.13 

45. 

25 

86 

87 

74.57 

44.81 

74.38 

45. 

13 

74. 

18 

45. 

46 

73.98 

45. 

78 

87 

88 

75.43 

45.32 

75.23 

45. 

65 

75. 

03 

45. 

98 

74.83 

46. 

31 

88 

89 

76.29 

45.84 

76.09 

46. 

17 

75. 

88 

46. 

50 

75.68 

48. 

83 

89 

90 

77.15 

46.35 

76.94 

46. 

69 

76. 

74 

47. 

02 

76.53 

47. 

36 

90 

91 

78.00 

46.87 

77.80 I 

47. 

21 

77. 

59 

47. 

55 

77.38 

47. 

89 

'91 

92 

78.86 

47.38 

78.65 

47. 

73 

78. 

44 

48. 

07 

78.23 

48. 

41 

92 

93 

79.72 

47.90 

79.51 

48. 

25 

79. 

30 

48. 

59 

79.08 

48. 

94 

93 

94 

80.57 

48.41 

80.36 

48. 

76 

80. 

15 

49. 

11 

79.93 

49. 

47 

94 

95 

81.43 

48.93 

81.22 

49. 

28 

81. 

00 

49. 

64 

80.78 

49. 

99 1 

95 

96 

82.29 

49.44 

82.07 

49. 

80 

81. 

85 

50. 

16 

81.63 

50. 

52 

90 

97 

83.15 

49.96 

82.93 

50. 

32 

82. 

71 

50. 

68 

82.48 

5:. 

04 

97 

98 | 

84.00 

50.47 

83.78 

50. 

S4 

83. 

56 

51. 

20 

83.33 

51. 

57 

98 

99 

84.86 , 

50.99 

84.64 

51. 

36 

84. 

41 

51. 

73 

84.18 

52. 

10 

99 

100 | 

85.72 I 

51.50 

85.49 

51 • 

88 

85. 

26 

52. 

25 

85.04 

52. 

62 

100 

6 

o 

£5 

Dep. | 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

d 

o 

c 

■«-> 

m 

• H 

Q 

59 Deg-. 

58| Deg. 

51H Deg. 

58i Deg. 

i 

| 

1 

cd 
—^ 

c n 

** 
























































































































66 


TRAVERSE TABLE. 


"1 

c 

►-*- 
U1 

r* 

p 

3 

o 

© 

32 Deg. 

32} Deg 

• 


32 £ 

Deg 


32} Deg. 

f Distance. 1 

[ 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0 

.85 

0 . 

53 

0.85 

0 . 

53 

0 

.84 

0 . 

54 

0 

.84 

0 . 

54 

1 

2 

1 

.70 

1 . 

06 

1.69 

1 . 

07 

1 

.69 

1 

07 

1 

.63 

1 . 

08 

2 

3 

2 

.54 

1 . 

59 

2.5 4 

1 . 

60 

2 

.53 

1 . 

61 

2 

.52 

1 . 

62 

3 

4 

3 

.39 

2 . 

12 

3.38 

2 . 

13 

3 

.37 

2 . 

15 

3 

.36 

& • 

16 

4 

5 

4 

.24 

2 . 

65 

4.23 

2 . 

67 

4 

.22 

2 . 

69 

4 

.21 

2 . 

70 

5 

6 

5 

.09 

3. 

18 

5.07 

3. 

20 

5 

.06 

3. 

22 

5 

.05 

3. 

25 

6 

7 

5 

.94 

3. 

71 

5.92 

3. 

74 

5 

.90 

3. 

76 1 

5 

.89 

3. 

79 

7 

8 

6 

.78 

4. 

24 

6.77 

4. 

27 

6 

.75 

4. 

30 j 

6 

.73 

4. 

33 

8 

9 

7 

.63 

4. 

77 

7.61 

4. 

80 

7 

.59 

4. 

84 

7 

.57 

4. 

87 

9 

10 

8 

.48 

5. 

30 

8.46 

5 . 

34 

8 

.43 

5. 

37 | 

8 

.41 

5. 

41 

10 

11 

9 

.33 

5. 

83 1 

9.30 

5. 

87 

9 

.28 

5. 

91 | 

9 

.25 

5. 

95 

11 

12 

10 

.18 

6 . 

36 j 

10.15 

6 . 

40 

10 

.12 

6 . 

45 

10 

.09 

6 . 

49 

12 

13 

11 

.02 

6 . 

89 ! 

10.99 

6 . 

94 

10 

.98 

5. 

98 

10 

.93 

7. 

03 

13 

14 

11 

.87 

7. 

42 

11.84 

7. 

47 

11 

.81 

7. 

52 

11 

.77 

i . 

57 

14 

15 

12 

.72 

7. 

95 

12.69 

8 . 

00 

12 

.65 

8 . 

08 

12 

.62 

8 . 

11 

15 

16 

13 

.57 

8 . 

48 i 

13.53 

8 . 

54 

13 

.49 

8 . 

60 

13 

.46 

8 . 

66 

16 

17 

14 

.42 

9. 

01 j 

14.38 

9. 

07 

14 

.34 

9. 

13 

14 

.30 

9. 

20 

17 

18 

15 

.26 

9. 

54 

15.22 

9. 

61 

15 

. 18 

9. 

67 

15 

.14 

9. 

74 

18 

19 

16 

.11 

10 . 

07 1 

16.07 

10 . 

14 

16 

.02 

10 . 

21 

15 

.98 

10 . 

23 

19 

20 

16 

.96 

10 . 

60 

16.91 

10 . 

67 

16 

.87 

10 . 

75 

16 

.82 

10 . 

82 

20 

21 

17 

.81 

11 . 

13 

17.7.6 

11 . 

21 

17 

.71 

11 . 

28 

17 

. 66 

11 . 

36 

21 

22 

18 

. 66 

11 . 

06 I 

18.61 

11 . 

74 

18 

.55 

11 . 

82 

18 

.50 

11 . 

90 

22 

23 

19 

.51 

12 . 

19 

19.45 

12 . 

27 

19 

.40 

12 . 

36 

19 

.34 

12 . 

44 

23 

24 

20 

.35 

12 . 

72 

20.30 

12 . 

81 

20 

.24 

12 . 

90 

20 

.18 

12 . 

93 

24 

25 

21 

.20 

13. 

25 

21.14 

13. 

34 

21 

.08 

13. 

43 

21 

.03 

13. 

52 

25 

26 

22 

.05 

13. 

78 

21.99 

13. 

87 

21 

.93 

13. 

9.7 

21 

.87 

14. 

07 

26 

27 

22 

.90 

14. 

31 

22.83 

14. 

41 

22 

.77 

14. 

51 

22 

.71 

14. 

Cl 

27 

28 

23 

.75 

14. 

84 

23.68 

14. 

94 j 

23 

.61 

15. 

04 

23 

. 55 

15. 

15 

28 

29 

24 

.59 

15. 

37 

I 24.53 

15. 

47 

24 

.46 

15. 

58 

24 

.39 

15. 

69 

29 

30 

25 

.44 

15. 

90 

!25.37 

16. 

on 

25 

.30 

16. 

12 i 

Arff J 

.23 

16. 

23 

30 

31 

26 

.29 

16. 

43 

26.22 

16. 

54 

26 

.15 

16. 

66 

or? 

At O 

.07 

16. 

77 

31 

32 

27 

. 14 

16. 

96 

27.06 

17. 

03 ! 

26 

.99 

17. 

19 

26 

.91 

17. 

31 

32 

33 

27 

.99 

17. 

49 

27.91 

17. 

61 

27 

.83 

17. 

73 

27 

.75 

17. 

85 

33 

34 

28 

.83 

18. 

02 

28.75 

18. 

14 

28 

.68 

13. 

27 

28 

.60 

18. 

39 

34 

35 

29 

.68 

18. 

55 

29.60 

18. 

68 

29 

. 52 

18. 

81 

29 

.44 

18. 

93 

35 

36 

30 

. 53 

13. 

08 

30.45 

19. 

21 

30 

.36 

19. 

34 

30 

.28 

19. 

48 

36 

37 

31 

.38 

19. 

61 

31.29 

19. 

74 

31 

.2! 

19. 

88 

31 

.12 

20 . 

02 

37 

33 

32 

.23 

20 . 

14 

32.14 

20 . 

23 

32 

.05 

20 . 

42 

31 

.96 

20 . 

56 

38 

39 

33 

.07 

20 . 

67 

32.93 

20 . 

81 

32 

.89 

20 . 

95 

32 

.80 

21 . 

10 

39 

40 

33 

.92 

21 . 

20 

33.83 

21 . 

31 

33 

.74 

21 . 

49 

33 

. 64 

21 . 

64 

40 

* 41 

34 

.77' 

o 1 

At 1 • 

73 

34.67 

21 . 

88 

34 

.58 

22 . 

03 

34 

.48 

22 . 

18 

41 

42 

35 

.62 

OO 

• 

26 

35.52 

09 

A4 At • 

41 

35 

.42 

22 . 

57 

35 

.32 

22 . 

72 

42 

43 

36 

.47 

22 . 

79 

36.37 

22 . 

95 

36 

.27 

23. 

10 

I 38 

.16 

23. 

26 

43 

44 

37 

.31 

23. 

32 

37.21 

23. 

48 

37 

.11 

23. 

64 

37 

.01 

23. 

80 

44 

45 

38 

.16 

23. 

85 

38.06 

24 

01 

37 

.95 

24. 

18 

37 

.85 


34 

45 

46 

39 

.01 

24. 

38 

38.90 

24. 

55 

38 

.80 

*>d 

<-WTC • 

72 

38 

.69 

94 

88 

46 

47 

39 

.86 

24. 

91 

39.75 

25. 

08 

39 

.64 

At»j • 

25 

39 

.53 

OR 

Ai*J 

43 

47 

48 

40 

.71 

25. 

44 

40.59 

25. 

61 

40 

.48 

25. 

79 

40 

.37 

25 

97 

48 

49 

41 

.55 

25. 

97 

41.44 

26. 

15 

41 

.33 

26. 

33 

41 

.21 

26 

51 

49 

50 

42 

.40 

26. 

50 

42.29 

26. 

68 

42 

.17 

20 . 

86 

j 42 

.05 

27. 

05 

50 

6 

w 

i 

r 

D 

ep. 

Lat. 

Dep. 

Lat. 

D 

ep. 

Lat. 

Dep. 

Lat. 

• 

C' 

c_ 

r * 

ri 

«-> 

m 

S 

58 Deg. 


57| Deg 

i 

57f Deg. 

r '•M 

bi t 

Deg. 



















































































































TRAVERSE TABLE. 


67 


a 

H' 

cc 

c-+ 

P 

32 Deg. 

32} Deg. 

32} Deg. 

32} Deg. 

O ! 

*— • * 

% 

3 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

D 

o 

? 

51 

43.25 

27.03 

43.13 

27.21 

43.01 

27.40 

42.89 

27.59 

5i 

52 

44.10 

27.56 

43.98 

27.75 

43.80 

27.94 

43.73 

28.13 

52 

53 

4-4.95 

28.09 

44.82 

28.28 

44.70 

28.48 

44.58 

28.67 

53 

54 

45.79 

28.62 

45.67 

28.82 

45.54 

29.01 

45.42 

29.21 

54 , 

55 

46.64 

29.15 

46.51 

29.35 

46.39 

29.55 

46.26 

29.75 

55 ' 

56 

47.49 

29.68 

47.36 

29.88 

47.23 

30.09 | 

47.10 

30.29 

56 

57 

48.34 

30.21 

48.21 

30.42 

48.07 

30.63 

47.94 

30.84 

57 

58 

49.19 

30.74 

49.05 

30.95 

48.92 

31.16 I 

48.78 

31.38 

58 

59 

50.03 

31.27 

49.90 

31.48 

49.76 

31.70 

49.02 

31.92 

59 

60 

50.88 

31.80 

50.74 

32.02 

50.60 

32.24 

50.46 

32.46 

60 

61 

51.73 

32.33 

51.59 

32.55 

51.45 

32.78 

51.30 

33.00 

61 

62 

52.58 

32.85 

52.44 

33.08 

52.29 

33.31 

52.14 

33.54 

62 

63 

53.43 

33.38 

53.28 

33.62 

53.13 

33.85 

52.99 

34.08 

63 

84 

54.28 

33.91 

54.13 

34.15 

53.98 

34.39 

53.83 

34.62 

64 

65 

55.12 

34.44 

54.97 

34.68 

54.82 

34.92 

54.67 

35.16 

65 

66 

55.97 

34.97 

55.82 

35.22 

55.66 

35.40 

55.51 

35.70 

66 

67 

56.82 

35.50 

56.66 

35.75 

56.51 

36.00 

56.35 

36.25 

67 

68 

57.67 

36.03 

57.51 

36.29 

57.35 

36.54 

57.19 

36.79 

68 

69 

58.52 

36.56 

58.36 

36.82 

58.19 

37.07 

58.03 

37.33 

69 

70 

59.36 

37.09 

59.20 

37.35 

59.04 

37.61 

58.87 

37.87 

70 

71 

60.21 

37.02 

60.05 

37.89 

59.88 

38.15 

59.71 

38.41 

71 

72 

61.06 

38.15 

60.89 

38.42 

60.72 

38.69 

60.55 

38.95 

72 

73 

61.91 

38.68 

61.74 

38.95 

61.57 

39.22 

61.40 

39.49 

73 

74 

62.76 

39.21 

62.58 

39.49 

62.41 

39.76 

62.24 

40.03 

74 

75 

63.60 

39.74 

63.43 

40.02 

63.25 

40.30 

I 63.08 

40.57 

75 

76 

64.45 

40.27 

64.28 

40.55 

64.10 

40.83 

i63.92 

41.11 

76 

77 

65.30 

40.80 

65.12 

41.09 

64.94 

41.37 

64.76 

41.65 

77 

78 

66.15 

41.33 

65.97 

41.62 

65.78 

41.91 

65.60 

42.20 

78 

79 

67.00 

41.86 

66.81 

42.16 

66.63 

42 45 

66.44 

42.74 

79 

80 

67.84 

42.39 

67.66 

42.69 

67.47 

42.98 

67.28 

43.28 

80 

81 

68.69 

42.92 

68.50 

43.22 

68.31 

43.52 

68.12 

43.82 

81 

82 

69.54 

43.45 

69.35 

43.76 

69.16 

44.06 

GS. 97 

44.36 

82 

83 

70.39 

43.98 

70.20 

44.29 

70.00 

44.60 

|69.81 

44.90 

83 

84 

71.24 

44.51 

71.04 

44.82 

70.84 

45.13 

70.65 

45.44 

84 

85 

72.08 

45.04 

71.89 

45.36 

71.69 

45.67 

|71.49 

45.98 

85 

86 

72.93 

45.57 

72.73 

45.89 

f72.53 

46.21 

72.33 

40.52 

86 

87 

73.78 

46.10 

73.58 

46.42 

|73.38 

46.75 

73.17 

47.06 

87 

88 

74.63 

46.63 

74.42 

46.96 

|74.22 

47.28 

74.01 

47.61 

88 

89 

75.48 

47.16 

75.27 

47.49 

75.06 

47.82 

174.85 

48.15 

89 

90 

76.32 

47.69 

76.12 

48.03 

75.91 

48.36 

75.09 

48.69 

90 

91 

77.17 

48.22 

76.96 

48.56 

76.75 

48.89 

176.53 

49.23 

91 

92 

78.02 

48.75 

77.81 

49.09 

77.59 

49.43 

77.38 

49 77 

92 

93 

78.87 

49.28 

78.65 

49.63 

78.44 

49.97 

78.22 

50.31 

93 

94 

79.72 

49.81 

79.50 

50.16 

79.28 

50.51 

79.06 

50.85 

94 

95 

80.56 

50.34 

80.34 

50.69 

80.12 

51.04 

79.90 

51.39 

95 

96 

81.41 

50.87 

81.19 

51.23 

80.97 

51.58 

80.74 

51.93 

96, 

97 

82.26 

51.40 

82.04 

51.76 

81.81 

52.12 

81.58 

52.47 

97 ' 

98 

83.11 

51.93 

82.88 

52.29 

82.65 

52.66 

82.42 

53.02 

98 

99 

83.96 

52.46 

83.73 

52.83 

83.50 

53.19 

!83.26 

53.56 

99 

100 

84.80 

52.99 

84.57 

53.36 

84.34 

53.73 

84.10 

54.10 

100 

r\ 

C 

a 

Dep. 

j Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

V \ 

r-i 

rt 

-4~> 

73 

/•*» 

U-4 

58 Deg. 

57} Deg. 

57} Deg. 

57} Deg. 

CO 

• ** 

a 




































































































68 


TRAVERSE TABLE. 


Distance. 

33 Deg. 

33} Deg. 

33} Deg 

• 


Deg. 

d 

5T 

r-* 

P 

2 

o 

*r> 

Lat. j 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0 

84 

0. 

54 

0. 

84 

0. 

55 

0. 

S3 

0. 

55 

b. 

83 

0.56 

1 

2 

1 

68 

1. 

09 

1. 

67 

1. 

10 

1. 

67 

1. 

10 

i. 

66 

1.11 

2 

3 

O 

52 

1. 

63 

2. 

51 

1. 

64 

2. 

50 

1. 

66 

Q 
a* • 

49 

1.67 

3 

4 

3 

.35 

O 
-w • 

18 

3. 

35 

2. 

19 

3. 

31 

2. 

21 

3. 

33 

2.22 

4 

5 

4 

.19 

2. 

72 | 

4. 

18 

2. 

74 

4. 

17 

o 

76 

4. 

IS 

2.78 

5 

6 

5 

.03 

3. 

27 j 

5. 

02 

3. 

29 

PL 

U 

00 

3. 

31 

4. 

99 

3.33 

6 

7 

5 

.87 

3. 

81 

5. 

85 

3 

84 

5. 

84 

3. 

86 

5. 

82 

3.89 

7 

8 

6 

71 

4. 

36 

6. 

69 

4. 

39 

6. 

67 

4. 

42 

6. 

65 

4.44 j 

8 

9 

7 

.55 

4. 

90 

7. 

53 

4. 

93 

7. 

50 

4. 

97 

7. 

48 

5.00 

9 

10 

8 

.39 

5. 

45 j 

8. 

36 

5. 

48 

8. 

34 

5. 

52 } 

8. 

31 

5.56 

10 

11 

9 

.23 

5. 

99 j 

9. 

20 

6. 

03 

9. 

17 

6. 

07 

9. 

15 

6.11 

11 

12 

10 

.06 

6. 

54 

10. 

04 

6. 

58 

10. 

01 

6. 

62 

9. 

98 

6.67 

12 

13 

10 

.90 

7. 

08 

10. 

87 

7. 

13 

10. 

84 

7. 

18 

10. 

81 

7.22 

13 

14 

11 

.74 

7. 

62 

11. 

71 

7. 

68 

11. 

67 

7. 

73 

11. 

64 

7.78 

14 

15 

12 

.58 

8. 

17 

12. 

54 

8. 

22 

12. 

51 

8. 

28 ; 

12. 

47 

8.33 

15 

16 

13 

.42 

8. 

71 

13. 

38 

8. 

77 

13. 

34 

8. 

#3 j 

13. 

30 

8.89 

16 

17 

14 

.26 

9. 

26 

14. 

22 

9. 

32 

14. 

18 

•J. 

38 

14. 

13 

9.44 

17 

18 

15 

.10 

9. 

80 

15. 

05 

9. 

87 

15. 

01 

9. 

93 

14. 

97 

10.00 

18 

19 

15 

.93 

10. 

35 

15 

89 

10. 

42 

15 

84 

10. 

49 

15. 

80 

10.56 

19 

20 

16 

.77 

10. 

89 

16. 

73 

10. 

97 

16 

68 

11 

04 j 

16. 

63 

11.11 

20 

21 

17 

.61 

11. 

44 

17 

56 

11. 

51 

17 

51 

11 

59 I 

17. 

46 

11.67 

21 

22 

18 

.45 

11. 

98 

18. 

40 

12. 

06 

18 

35 

12 

14 

18. 

29 

12.22 

22 

23 

19 

.29 

12. 

53 

19 

23 

12. 

61 

19 

18 

12 

69 j 

19. 

12 

12.73 

23 

24 

20 

13 

13. 

07 

20 

07 

13 

16 

20 

01 

13. 

25 

19. 

96 

13.33 

24 

25 

20 

.97 

13. 

62 

20 

91 

13 

71 

20 

85 

13. 

80 

20. 

79 

13.89 

25 

26 

21 

.81 

14. 

16 

21 

74 

14 

26 

21 

68 

14 

35 

21 

62 

14.44 

26 

27 

22 

.64 

14. 

71 

22 

.58 

14 

80 

22 

.51 

14 

90 

22 

45 

15.00 

27 

28 

23 

.48 

15. 

25 

23 

.42 

15 

35 

23 

35 

15 

45 

23 

OQ 

15.56 

23 

29 

24 

.32 

15. 

79 

24 

25 

15 

00 

24 

.18 

16 

01 

24 

11 

16.11 

29 

30 

25 

. 16 

16. 

34 

25 

.09 

16 

.45 

25 

.02 

16 

.56 

24 

94 

16.67 

30 j 

31 

26 

.00 

16. 

88 

25 

.92 

17 

.00 

25 

.85 

17 

.11 

25 

78 

17.22 

31 

32 

26 

.84 

17. 

43 

26 

.76 

17 

.55 

1 26 

.68 

17 

66 

26 

61 

17.78 

32 

33 

27 

.68 

17. 

97 

27 

.60 

18 

.09 

27 

.52 

18 

.21 - 

27 

.44 

18.33 

33 

34 

28 

.51 

IS. 

52 

28 

.43 

18 

64 

28 

.35 

18 

.77 

28 

.27 

13.89 

34 

35 

29 

.35 

19. 

06 

29 

.27 

19 

.19 

29 

.19 

19 

.32 

29 

.10 

19.44 

35 

36 

30 

. 19 

19. 

61 

30 

.11 

19 

.74 

30 

.02 

19 

.87 

29 

93 

20.00 

36 

37 

■n 

.03 

20. 

15 

30 

.94 

20 

.29 

30 

.85 

20 

.42 

30 

.76 

20.56 

i 37 

38 

31 

.87 

20. 

70 

31 

.78 

20 

.84 

31 

.69 

20 

.97 

31 

.60 

21.11 

! 33 

39 

32 

71 

21. 

24 

32 

.62 

21 

.38 

32 

.52 

21 

.53 

32 

.43 

21.67 

1 39 

40 

33 

.55 

21. 

79 

33 

.45 

21 

.93 

33 

.36 

22 

.08 

33 

.26 

22.22 

1 40 

41 

34 

.39 

oo 

'/J 

33 

34 

.29 

22 

.48 

34 

.19 

22 

.63 

34 

.09 

j22.78 

j 41 

42 

35 

.22 

22 

87 

35 

. 12 

23 

.03 

35 

.02 

23 

.18 

34 

.92 

! 23.33 

' 42 

43 

36 

.06 

23 

42 

35 

.96 

23 

.58 

35 

.86 

23 

.73 

1 35 

.75 

i23.89 

43 

44 

36 

.90 

23 

96 

36 

.80 

24 

. 12 

36 

.69 

24 

.29 

36 

.58 

24.45 

i 44 

45 

37 

.74 

24 

51 

37 

.63 

24 

.67 

37 

.52 

24 

.81 

37 

.42 

25 00 

i 45 

46 

38 

.58 

25 

05 

38 

.47 

25 

.22 

38 

.36 

25 

.39 

33 

.25 

25.56 

46 

47 

39 

.42 

25 

60 

39 

.31 

25 

.77 

39 

.10 

i 25 

.94 

39 

.08 

26.11 

1 47 

48 

40 

.26 

26 

.14 

40 

.14 

26 

.32 

40 

.03 

26 

.49 

39 

.91 

i26.67 

| 48 

49 

41 

.09 

26 

.69 

40 

.98 

26 

.87 

40 

.86 

27 

.04 

40 

. 74 

!27.22 

| 49 

50 

41 

.93 

27 

.23 

41 

.81 

27 

.41 

41 

.69 

27 

.60 

41 

.57 

27.78 

j 50 

a> 

c 

a 

c6 

(/} 

• H 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 

Dep. 

Lat. 

~ 

i c 


57 

Deg 

• 

56} Deg. 

■ H*.' 

56} Deg. 

56J Deg. 

CC 















































































































TRAVERSE TABLE. 


69 


7) 

—1 

P 

33 Deg. 


33* De 



33* 

Deg. 

33| Deg. 

Vu 

P 

o 

o 

Lat. 

Dep. 

L 

at. 

Dep. 

Lclt* 

Dep. 

Lat. 

Dep. 

Q 

CD 

51 

42 

.77 

27. 

78 

42 

.65 

27 

.96 

42 

.53 

28. 

15 

42 

.40 

28. 

33 

51 

52 

43 

.61 

28. 

32 

43 

.49 

28 

.51 

43 

.36 

28. 

70 

43 

.24 

28. 

89 

52 

53 

44 

.45 

28. 

87 

44 

.32 

29 

.06 

44 

.20 

29. 

25 

44 

.07 

29. 

45 

53 

54 

45 

.29 

29. 

41 

45 

.16 

29 

.61 

45 

.03 

29. 

80 

44 

.90 

30. 

00 

54 

55 

46 

.13 

29. 

96 

46 

.00 

30 

.16 

45 

.86 

30. 

36 

45 

.73 

30. 

56 

55 

56 

46 

.97 

30. 

50 

46 

.83 

30 

.70 

46 

.70 

30. 

91 

46 

.56 

31. 

11 

56 

57 

47 

.80 

31. 

04 

47 

.07 

31 

.25 

47 

.53 

31. 

46 

47 

.39 

31. 

67 

57 

58 

43 

.64 

31. 

59 

48 

.50 

31 

.80 

48 

.37 

32. 

01 i 

48 

.23 

32. 

22 

58 

59 

49 

.48 

32. 

13 

49 

.34 

32 

.35 

49 

.20 

32. 

56 

49 

. 06 

32. 

78 

59 

60 

50 

.32 

32. 

68 

50 

.18 

32 

.90 

50 

.03 

33. 

12 

49 

.89 

QO 

33 

60 

61 

51 

.16 

33. 

22 

51 

.01 

33 

.45 

50 

.87 

33. 

67 

50 

.72 


89 

61 

62 

52 

.00 

33. 

77 

51 

.85 

33 

.99 

51 

.70 

34. 

22 

51 

.55 

34. 

45 

62 | 

63 

52 

.84 

34. 

31 

52 

.69 

34 

.54 

52 

.53 

34. 

77 

52 

.38 

35. 

00 

63 1 

64 

53 

.67 

34. 

86 

53 

.52 

35 

.09 

53 

.37 

35. 

32 

53 

.21 

35. 

56 

641 

65 

54 

.51 

35. 

40 

54 

.36 

35 

.64 

54 

.20 

35. 

88 

54 

.05 

36. 

11 

65 I 

66 

55 

.35 

• 

95 

55 

.19 

36 

.19 

55 

.04 

36. 

43 

54 

.88 

36. 

67 

VS | 

67 

56 

. 19 

36. 

49 

56 

.03 

36 

.74 

55 

.87 

36. 

98 

55 

.71 

37. 

22 

67 1 

68 

57 

.03 

37. 

04 

56 

.87 

37 

.28 

56 

.70 

37. 

53 

56 

.54 

37. 

78 

68 

69 

57 

.87 

37. 

58 

57 

.70 

37 

.83 

57 

.54 

38. 

08 

57 

.37 

38. 

33 

69 

70 

58 

.71 

38. 

12 

58 

.54 

38 

.38 

58 

.37 

38. 

64 

58 

.20 

38. 

89 

70 

71 

59 

.55 

38. 

67 

59 

.38 

38 

.93 

59 

.21 

39. 

19 

59 

.03 

39. 

45 

71 

72 

60 

.38 

39. 

21 

60 

.21 

39 

.48 

60 

.04 

39. 

74 

59 

.87 

40. 

00 

72 

73 

61 

.22 

39. 

76 

61 

.05 

40 

.03 

60 

.87 

40. 

29 

60 

.70 

40. 

56 

73 

74 

62 

.06 

40. 

30 

61 

.89 

40 

.57 

61 

.71 

40. 

84 

61 

.53 

41. 

11 

74 

75 

62 

.90 

40. 

85 

62 

.72 

41 

.12 

62 

.54 

41. 

40 

62 

.36 

41. 

67 

75 

76 

63 

.74 

41. 

39 

63 

.56 

41 

.67 

63 

.38 

41. 

95 

63 

.19 

42. 

22 

76 

77 

64 

.58 

41. 

94 

64 

.39 

42 

.22 

64 

.21 

42. 

50 

64 

.02 

42. 

78 

77 

78 

65 

.42 

42. 

48 

65 

.23 

42 

.77 

65 

.04 

43. 

05 

64 

.85 

43. 

33 

78 

79 

66 

.25 

43. 

03 

66 

.07 

43 

.32 

65 

.88 

43. 

60 

65 

.69 

43. 

89 

79 

80 

67 

.09 

43. 

57 

66 

.90 

43 

.86 

66 

.71 

44. 

15 

66 

.52 

44. 

45 

80 | 

81 

67 

.93 

44. 

12 

67 

.74 

44 

.41 

67 

.54 

44. 

71 

67 

.35 

45. 

00 

81 

82 

68 

.77 

44. 

66 

68 

.58 

44 

.96 

68 

.38 

45. 

26 

68 

.18 

45 

56 

82 

83 

69 

.61 

45. 

20 

69 

.41 

45 

.51 

69 

.21 

45. 

81 

69 

.01 

46. 

11 

83 

84 

70 

.45 

45. 

75 

70 

.25 

46 

.06 

70 

.05 

46. 

36 

69 

.84 

46. 

67 

84 

\ 85 

71 

.29 

46. 

29 

71 

.OS 

46 

.60 

70 

.88 

46. 

91 

70 

.67 

47. 

22 

85 

86 

72 

. 13 

46. 

84 

71 

.92 

47 

.15 

71 

.71 

47. 

47 

71 

.51 

47. 

78 

86 

87 

72 

.96 

47. 

38 

72 

.76 

47 

.70 

72 

.55 

48. 

02 

72 

.34 

48. 

33 

87 

88 

73 

.80 

47. 

93 

73 

.59 

48 

.25 

73 

.38 

48. 

57 

73 

.17 

48. 

89 

88 

89 

74 

.64 

4-8. 

47 

74 

.43 

48 

.80 

74 

.22 

49. 

12 

1 74 

.00 

49. 

45 

89 

90 

75 

.48 

49. 

02 

75 

.27 

49 

.35 

75 

.05 

49. 

67 

I 74 

.83 

50. 

00 

90 

91 

70 

.32 

49. 

56 

76 

.10 

49 

.89 

75 

.88 

50. 

23 

75 

.66 

50. 

56 

91 1 

92 

77 

. 16 

50. 

11 

76 

.94 

50 

.44 

76 

.72 

50. 

78 

1 76 

.50 

51 

11 

92 i 

93 

78 

.00 

50. 

65 

' 77 

.77 

50 

.99 

77 

.55 

51. 

QO 

oo 

I 77 

.33 

51 

67 

93 

94 

78 

.83 

51. 

20 

1 78 

.61 

51 

.54 

78 

.39 

51. 

88 

78 

.16 

52 

22 

94 

95 

79 

.67 

51. 

74 

i 79 

.45 

52 

.09 

79 

.22 

52. 

43 

78 

.99 

52 

.78 

95 ! 

ij 96 

80 

.51 

52 

29 

i 80 

.28 

52 

.64 

80 

.05 

52 

99 

79 

.82 

53 

.33 

96 

J 97 

31 

.35 

52. 

83 

1 81 

.12 

53 

. 18 

80 

.89 

53 

54 

80 

.65 

53 

.89 

97 

j 98 

82 

. 19 

53 

37 

1 81 

.96 

53 

.73 

81 

.72 

54. 

09 

81 

.48 

54 

.45 

* 98 

99 

83 

.03 

53. 

92 

j 82 

.79 

54 

.28 i 

82 

.55 

54 

64 

82 

.32 

55 

.00 

99 I 

100 

S3 

.87 

54. 

46 

! 83 

.63 

54 

.83 

S3 

.39 

55 

19 

83 

.15 

55 

56 

! 00 

6 

o 

c, 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L 

at. 

Dep. 

Lat. 

j p 

1 g 

d 

'/> 

J-J 


57 Deg. 



561 

Deg. 

56* Deg. 


564 

Deg. 

_ 

Cw 

7. 























































































































TRAVERSE lA/iLE. 


'0 


1 

p 

5 1 

p 

3 

a 

o 

34 Deg. 

34^ Deg. 

34^ 

Deg. 

34? Deg. 

p 

7. 

p 

Lat. 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

“T 

0.83 

0.56 

0.83 

0.56 

0.82 

0.57 

0 . 82 

C .57 

1 

2 

1.66 

1.12 

1.65 

1.13 

1.65 

1.13 

1.64 

1.14 

2 

3 

2.49 

1.68 

2.48 

1.69 

2.47 

1.70 

2.46 

1.7! 

3/ 

4 

3.32 

2.24 

3.31 

2.25 

3.30 

2.27 

3.29 

2.28 

4 

5 ; 

4.15 

2.80 

4.13 

2.81 

4.12 

2.83 

4.11 

2.85 

0 { 

6 

4.97 

3 • 36 

4.96 

3.38 

4.94 

3.40 

4.93 

3.42 

f.l 

7 

5.80 

3.91 

5.79 

3.94 

5.77 

3.96 

5.75 

3.99 

7 

8 

6.63 

4.47 

6.61 

4.50 

6.59 

4.53 

6.57 

4.56 

§ 

9 

7.46 

5.03 

7.44 

5.07 

7.42 

5.10 

7.39 

1.13 

9 

10 

8.29 

5.59 

8.27 

5.63 

8.24 

5.66 

8.22 

5.70 

10 

11 

9.12 

6.15 

9.09 

6.19 

9.07 

6.23 

9.04 

6.27 

11 

12 

9.95 

6.71 

9.92 

6.75 

9.89 

6.80 

9.86 

6.84 

12 

13 

10.78 

7.27 

10.75 

7.32 

10.71 

7.36 

10.68 

7.41 

13 

14 

11.61 

7.83 

11.57 

7.88 

11.54 

7.93 

11.50 

7.98 

14 

15 

12.44 

8.39 

12.40 

8.44 

12.36 

8.50 

12.32 

8 .55 

15 

16 

13.26 

8.95 

13.23 

9.00 

13.19 

9.06 

13.15 

9.12 

16 

17 

14.09 

9.51 

14.05 

9.57 

14.01 

9.63 

13.97 

9.69 

17 

18 

14.92 

10.07 

14.88 

10.13 

14.83 

10.20 

14.79 

10.26 

18 

19 

15.75 

10.62 

15.71 

10.69 

15.66 

10.76 

15.61 

10.83 

19 

20 

16.58 

11.18 j 

16.53 

11.26 

16.48 

11.33 | 

16.43 

11.40 

20 

21 

17.41 

11.74 ] 

17.36 

11.82 

17.31 

11.89 

17.25 

11.97 

21 

22 

18.24 

12.30 ! 

18.18 

12.38 

18.13 

12.46 

18.08 

12.54 

22 

23 

19.07 

12.86 | 

19.01 

12.94 

18.95 

13.03 | 

18.90 

13.11 

23 

24 

19.90 

13.42 

i19.84 

13.51 

19.78 

13.59 

19.72 

13.68 

24 

25 

20.73 

13.98 

20.66 

14.07 

20.60 

14.16 

20.54 

14.25 

25 

26 

21.55 

14.54 

21.49 

14.63 

21 .43 

14.73 

21.36 

14.82 

26 

27 

22.38 

15.10 

22.32 

15.20 

22.25 

15.29 

22.18 

15.39 

27 

28 

23.21 

15 66 

23.14 

15.76 

23.08 

15.86 

23.01 

15.96 

28 

29 

24.04 

16.22 

23.97 

16.32 

23.90 

16.43 

23.83 

16.53 

29 

30 

24.87 

16.78 

24.80 

16.88 

24.72 

16.99 

24.65 

17.10 

30 

31 

25.70 

17.33 

25. G2 

17.45 

25.55 

17.56 

25.47 

17.67 

31 

32 

26.53 

17.89 

26.45 

18.01 

26.37 

18.12 

26.29 

18.24 

32 

33 

27.36 

18.45 

27.28 

18.57 

27.20 

18.69 

27.11 

18.81 

33 

34 

28.19 

19.01 

28.10 

19.14 

28.02 

19.26 

27.94 

19.38 

34 

35 

29.02 

19.57 

28.93 

19.70 

28.84 

19.82 

28.70 

19.95 

35 

36 

29.85 

20.13 

29.76 

20.26 

29.67 

20.39 

29.58 

20.52 

36 

37 

30.67 

20.69 

30.58 

20.82 

30.49 

20.96 

30.40 

21.09 

3* 

38 

31.50 

21.25 

31.41 

21.39 

31.32 

21.52 

31.22 

21.66 

39 

39 

32.33 

21.81 

32.24 

21.95 

32.14 

22.09 

32.04 

22.23 

39 

40 

33.16 

22.37 

33.06 

22.51 

32.97 

22. G6 

32.87 

22.80 

40 

41 

33.99 

22.93 

33 . 89 

23.07 

33.79 

23.22 

33 . 69 

23.37 

41 

42 

34.82 

23.49 

34.72 

23.64 

34.61 

23.79 

34.51 

23.94 

42 

43 

35.65 

24.05 

!36.54 

24.20 

35.44 

24.36 

35.33 

24.51 

43 

44 

36.48 

24.60 

136.37 

24.70 

36.26 

24.92 

36.15 

25.08 

44 

45 

37.31 

25.16 

137.20 

25.33 

37.09 

25.49 

36.97 

25.65 

45 

46 

38.14 

25.72 

138.02 

25.89 

37.91 

26.05 

! 37.80 

1 26.22 

46 

47 

38 . 96 

26.28 

I 38.85 

26.45 

38.73 

26.62 

38.62 

26.79 

47 

48 

i 39 . 79 

26.84 

i 39.68 

i 27.01 

39.56 

27.19 

39.44 

27.36 

48 

49 

I 40.62 

27.40 

40.50 

' 27.58 

40.38 

27.75 

40.26 

27.93 

49 

50 

1 41.45 

| 27.96 

41.33 

|28.14 

41.21 

28.32 

41.08 

28.50 

50 

Distance. 

Dep. 

1 T 

Lat. 

Dep. 

! Lat. 

Dep. 

Lat. 

Dep. 

Lat. 


56 Deg. 

55? Deg. 

55A 

Deg. 

o'v? Deg. 

5 

L 

i£ 

i»_ 

< 


uTt —.. „ . _ 






i 























































































































TRAVERSE TABLE 


71 


r 

W 

►-» 

Vi 

<—• 

P 

1 

34 

Deg 



34 \ 

Deg. 

1 

341 

Deg. 


341 

Deg. 

O 

5* 

3 

O 

» 

L 

at. 

j Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

L 

tit. 

Dep. 

P 

O 

P 

51 

42 

.28 

28 

.52 

42 

.16 

28 

.70 

42 

.03 

28 

89 

41 

.90 

29 

.07 

1 si 

52 

43 

.11 

29 

.08 

42 

.98 

j 29 

.27 

42 

.85 

29 

45 

42 

.73 

29 

.64 

i 52 

53 

43 

.94 

29 

.64 

43 

.81 

i 29 

83 

43 

.68 

30 

02 

43 

. 55 

30 

21 

> 53 

54 

44 

.77 

30 

.20 

44 

.64 

1 30 

39 

44 

.50 

30 

59 

44 

.37 

30 

78 

54 

55 

45 

.60 

30 

.76 

45 

.46 

1 30 

95 

| 45 

.33 

31 

15 

45 

.19 

31 

35 

55 

56 

46 

.43 

31 

.31 

46 

.29 

j 31 

52 

! 46 

.15 

31 

72 

1 46 

01 

31 

92 

56 

5? 

47 

.26 

31 

.87 

47 

. 12 

32 

08 

j 46 

.98 

32 

29 

j 46 

.83 

32 

49 

57 

58 

48 

.08 

32 

.43 

47 

.94 

32 

64 

47 

.80 

32. 

85 

47 

.66 

33 

06 

58 

59 

48 

.91 

32 

.99 

48 

.77 

I 33 

21 

48 

.62 

33. 

42 

48 

.48 

33 

63 

59 

60 

49 

.74 

33 

.55 

49 

.60 

! 33 

77 

49 

.45 

33. 

98 

49 

.30 

34. 

20 

60 

6 i 

50 

.57 

34 

.11 

50 

.42 

' 34. 

33 

50~ 

.27 

34. 

55 

50 

.12 

34. 

77 

61 

62 

51 

.40 

34 

.67 

M 

. 25 

34 

89 

51 

.10 

35 

12 

50 

.94 

35. 

34 

62 

63 

52 

.23 

35 

.23 

1 52 

.08 

35 

46 

5 1 

.92 

35 

68 

51 

.76 

35 

91 

63 

64 

53 

.06 

35 

. 79 

52 

.90 

36. 

02 


.74 

36 

25 ! 

52 

.59 

36 

48 

64 

65 

53 

.89 

36 

.35 

53 

.73 

36. 

58 

i 53 

. 57 

36. 

82 

53 

.41 

37. 

05 

65 

66 

54 

.72 

36 

.91 

54 

.55 

37. 

15 

1 54 

.39 

37. 

38 

54 

.23 

37. 

62 

66 

67 

55 

. 55 

37 

.46 

55 

.38 

37. 

71 

55 

.22 

37. 

95 

55 

. 05 

38. 

19 

67 

68 

56 

.37 

38 

.03 

56 

.21 

38. 

27 

56 

.04 

38. 

52 

55 

.87 

38. 

76 

68 

69 

57 

.20 

38 

.58 

57 

.03 

38. 

83 

56 

.86 

39. 

08 

56 

.69 

39. 

33 

69 

70 

58 

.03 

39 

. 14 

57 

.86 

39. 

40 

57 

.69 

39. 

65 

57 

.52 

39. 

90 

70 

71 

1 58 

.86 

39 

.70 

58 

.69 

39. 

96 

58 

.51 

40. 

21 

58 

.34 

40. 

47 

71 

72 

59 

.69 

40 

.26 

59 

.51 

40. 

52 

59 

.34 

40. 

78 

59 

.16 

41 . 

04 

72 

73 

60 

.52 

40 

.82 

60 

.34 

41 

08 

60 

.16 

41. 

35 

59 

. 9S 

41. 

61 

73 

74 

61 

.35 

41 

.38 

61 

.17 

41. 

65 

60 

.99 

41. 

91 

60 

.80 

42. 

18 

74 

75 

62 

.18 

41 

.94 

61 

.99 

42. 

21 

61 

.81 

42. 

48 

61 

.62 

42. 

75 

75 

76 

63 

.01 

42 

.50 

62 

.82 

42. 

77 

62 

.63 

43. 

05 

62 

.45 

43. 

32 

76 

77 

63 

.84 

43 

.06 

63 

.65 

43. 

34 

63 

.46 

43. 

61 

63 

.27 

43. 

89 

77 

78 

64 

66 

43 

.62 

64 

.47 

43. 

90 

64 

.28 

44. 

18 

64 

.09 

44. 

46 

78 

79 

65 

.49 

44 

.18 

65 

30 

44. 

46 

65 

.11 

44. 

75 

64 

.91 

45. 

03 

79 

80 

66 

.32 

44 

.74 

66 

13 

45. 

02 

65 

.93 

45. 

31 

65 

.73 

45. 

60 

80 

81 

67 

.15 

45 

.29 

66 

95 

45. 

59 

66 

.75 

45. 

88 

66 

55 

46. 

17 

81 

82 

67 

98 

45 

.85 

67 

78 

46. 

15 

67 

.58 

46. 

45 

67 

.37 

46. 

74 

82 

83 

68 

81 

46 

.41 

68 

61 

46. 

71 

68 

.40 

47. 

01 

68 

.20 

47. 

31 

83 

84 

69 

64 

46 

.97 

69 

43 

47. 

28 

69 

.23 

47. 

58 

69 

.02 

47. 

88 

84 

85 

70 

47 

47 

53 

70 

26 

47. 

84 

70 

.05 

48. 

14 

69 

.84 

48. 

45 

85 

86 

71 

30 

48 

09 

71 

09 

48. 

40 

70 

.87 

48. 

71 

70 

.66 

49. 

02 

86 

87 

72 

13 

48 

65 

71 

91 

48. 

96 

71 

.70 

49. 

28 

71 

.48 

49. 

59 

87 

88 

72 

96 

49 

21 

72 

74 

49. 

53 

72 

.52 

49. 

84 

72 

.30 

50. 

16 

88 

89 

73. 

78 

49 

77 

73 

57 

50. 

09 

73 

.35 

50. 

41 

73 

13 

50 

73 

89 

90 

74. 

61 

50 

33 

74 

39 

50. 

65 

74 

17 

50. 

98 

73 

.95 

51 . 

30 

90 

91 

75. 

44 

50 

89 

75. 

22 

51. 

22 

75 

.00 

51. 

54 

74 

.77 

51. 

87 

91 

92 

76. 

27 

51 

45 

76. 

05 

51. 

78 

75 

.82 

52. 

11 

75 

.59 

52. 

44 

92 

93 

77. 

10 

52. 

00 

76. 

87 

KO 
* J /*-< • 

34 

76 

.64 

52. 

68 

76 

.41 

53. 

01 

93 

94 

77. 

93 

52 

56 

77. 

70 

52. 

90 

77 

.47 

53. 

24 

77 

.23 

53. 

58 

94 

95 

78. 

76 

53 

12 

78. 

53 

53. 

47 

78 

.29 

53. 

81 

78 

.06 

54. 

15, 

95 

96 

79. 

59 

53. 

68 

79. 

35 

54. 

03 

79 

.12 

54. 

37 

78 

.88 

54. 

72 

96 

97 

80. 

42 

54. 

24 

80. 

18 

54. 

59 

79 

.94 

54. 

94 

79 

70 

55. 

29 

97 

98 

81. 

25 

54. 

80 

81. 

01 

55. 

15 

80 

76 

55. 

51 

80 

52 

55. 

86 

98 

99 

82. 

07 

55. 

36 

81. 

83 

55. 

72 

81 

59 

56. 

07 

81 

.34 

56. 

43 

99 

100 

82. 

90 

55. 

92 

82. 

66 

56. 

28 

82 

.41 

56. 

64 

82 

.16 

57. 

00 

100 

• 

o 

o 

c 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

a! 

o 

a 

rd 

Vi 

• H 

Q 

56 Deg, 

% 

551 Deg. 

55j Deg 


55} 

Deg 


cd 

■4~> 

Vi 

5 















































































































72 


TRAVERSE TABLE 


g 

5* 

P 

3 

O 

CD 

35 Deg. I 

35$ Deg. 

P- 

35$ Deg. 

35f Deg. J 

U 

M • 

08 

c-+ 

PS 

Lat. 

Dep. 

Lat. 

De 

Lat. 

Dep. 

Lat. 

Dep. j 

3 

o 

a 

1 

0. 

82 

0. 

57 

0.82 

0. 

58 

0.81 

0.58 

0.81 

0.58 

1 

o 

1. 

64 

1. 

15 

1.63 i 

1. 

15 

1.63 

1.16 

1.62 

1.17 

2 

3 

2. 

46 j 

1. 

72 

2.45 j 

1. 

73 

2.44 

1.74 

2.43 

1.75 ' 

3 

1 

5 

3. 

28 

O 

29 

3.27 1 

2. 

31 

3.26 

2.32 

3.25 

2.34 • 

4 

4. 

10 ! 

2. 

87 

4.08 ; 

2. 

89 

4.07 

2.90 

4.06 

2.92 

5 

6 

4. 

91 1 

3. 

44 

4.90 | 

3. 

46 1 

4.88 i 

3.48 

4.87 

3.51 | 

6 

7 

5. 

73 

4. 

01 

5.72 1 

4. 

04 1 

5.70 

4.06 

5.68 

4.09 

7 

8 

6. 

55 1 

4. 

59 

6.53 

4. 

62 

6.51 

4.65 

6.49 

4.67 

3 

9 

7. 

37 

5. 

16 

7.35 

5. 

19 

7.33 

5.23 

7.30 

5.26 

9 

10 

8. 

19 

5. 

74 

8.17 

5. 

77 

8.14 

5.81 

8.12 

5.84 

10 

" 11 

9. 

01 

6. 

31 

8.98 

6. 

35 

8.96 

6.39 

8.93 

6.43 

ii : 

12 

9. 

83 

6. 

88 

9.80 

6. 

93 

9.77 

6.97 

9.74 

7.01 

12 

13 

10. 

65 

7. 

46 

10.62 

7. 

50 

10.58 

7.55 

10.55 

7.60 

13 

14 

11. 

47 

8. 

03 

11.43 

8. 

08 

11.40 

8.13 

11.36 

8.18 

14 

15 

12. 

29 

8. 

60 

12.25 

8. 

66 

12.21 

8.71 

12.17 

8.76 

15 

16 

13. 

11 

9. 

18 

13.07 

9. 

23 

13.03 

9.29 

12.99 

9.35 

16 

17 

13. 

93 

9. 

75 

13.83 

9. 

81 

13.84 

9.87 

13.80 

9.93 

17 

18 

14. 

74 

10. 

32 

14.70 

10. 

39 

14.65 

10.45 

14.61 

10.52 

18 

19 

15. 

56 

10. 

90 

15.52 

10. 

97 

15.47 

11.03 

15.42 

11.10 

19 

2Qi 

16. 

38 

11. 

47 

16.33 

11. 

54 

16.28 

11.61 

16.23 

11.68 

20 

21 

17. 

20 

12. 

05 

17.15 

12. 

12 

17.10 

12.19 

17.04 

12.27 

21 

22 

18. 

02 

12. 

62 

17.97 

12. 

70 

17.91 

12.78 

17.85 

12.85 

22 

23 

18. 

84 

13. 

19 

18.78 

13. 

27 

18.72 

13.36 

18.67 

13.44 

23 

24 

19. 

66 

13. 

77 

19.60 

13. 

85 | 

19.54 

13.94 

19.48 

14.02 

24 

25 

20. 

48 

14. 

34 

20.42 

14. 

43] 

20.35 

14.52 

20.29 

14.61 

25 

26 

21. 

30 

14. 

91 

21.23 

15. 

O' 

21.17 

15.10 

21.10 

15.19 

26 

27 

22. 

12 

15. 

49 j 

22.05 

15. 

58 

21.98, 

15.68 

i21.91 

15.77 

27 

28 

22 

94 

16 

06 

22.87 

16. 

16 j 

22.80 

16.26 

22.72 

16.36 

23 

29 

23 

76 

16 

63 

23.68 

16 

74 

23.61 

16.84 

23.54 

16.94 

29 

30 

Oj_ 

/C/r 

57 

17 

21 

24.50 

17 

31 

24.42 

17.42 

|24.35 

17.53 

30 

31 

25 

39 

17 

78 i 

25.32 

17 

89 

25.24 

18.00 

25.16 

18.11 

31 

32 

26 

21 

18 

35 

26.13 

18 

47 

26.05 

18.58 

25.97 

18.70 

32 

33 

27 

.03 

18 

93 

26.95 

19 

05 

26.87 

19.16 

26.78 

19.28 

33 

34 

35 

27 

.85 

19 

50 

27.77 

19 

.62 

27.68 

19.74 

27.59 

19.86 

34 

28 

.67 

20 

08 

28.58 

20 

.20 

28.49 

20.32 

28.41 

20.45 

35 

36 

29 

.49 

20 

65 

29.40 

1 20 

.78 

29.31 

20.91 

29.22 

21.03 

36 

37 

30 

.31 

21 

.22 

30.22 

I 21 

.35 

30.12 

i21.49 

30.03 

21.62 

37 

38 

31 

.13 

21 

.80 

31.03 

21 

.93 

30.91 

|22.07 

30.84 

22.20 

38 

39 

31 

.95 

22 

.37 

31.85 

22 

.51 

31.75 

22.65 

31.65 

22.79 

39 

40 

1 32 

.77 

22 

.94 

32.67 

23 

.09 

32.56 

23.23 

32.46 

oo 0*7 

40 

41 

33 

.59 

23 

752 

33.48 

23 

.66 

33.3S 

23.81 

33.27 

23.95 

41 

42 

34 

.40 

24 

.09 

34.30 

24 

.24 

34.19 

24.39 

1 34.09 

24.54 

42 

43 

i 35 

.22 

24 

.66 

35.12 

24 

.82 

35.01 

24.97 

34.90 

25.12 

43 

44 

1 36 

.04 

25 

.24 

35.93 

25 

.39 

35.82 

25.55 

! 35.71 

25.71 

44 

45 

j 36 

.86 

25 

.81 

36.75 

25 

.97 

36.64 

26.13 

36.52 

26.29 

45 

46 

1 37 

.68 

26 

.38 

37.57 

! 26 

.55 

37.45 

26.71 

37.33 

26.88 

46 

47 

38 

.50 

26 

.96 

38.38 

i 27 

.13 

38.26 

27.29 

38.14 

27.46 

47 

48 

! 39 

.32 

27 

.53 

39.20 

27 

.70 

39.08 

27.87 

38.96 

1 28.04 

48 

49 

40 

. 14 

! 28 

. 11 

40.02 

28 

.28 

39.89 

28.45 

39.77 

j 28.63 

49 

50 

40 

.96 

28 

.68 

40.83 

1 28 

.86 

40.71 

29.04 

40.58 

29.21 

50 

| Distance. j 

Dep. 

Lat. 

Dep. 

j Lat. 

Dep. 

j Lat. 

j Dep. 

( Lat. 

1 

Distance. 1 

55 Deg. 

54J Deg. 

1 

54.$ Deg. 

J 54$ Deg 










































































































TRAVERSE TABLE. 


73 


Distance.|, 

35 Deg. 

35^ Deg. 

35^ Deg. 

351 Deg. 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

I Dep. 

Lat. 

Dep. 

01 

41.78 

29.25 

41.65 

29.43 

41.52 

129.62 

41.39 

29.80 

i 51 

52 

42.60 

29.83 

42.47 

I 30.01 

42.33 

130.20 

42.20 

30.38 

I 52 

53 

43.42 

30.40 

43.28 

30.59 

43.15 

30.78 

43.01 

30.97 

1 53 

54 

44.23 

30.97 

44.10 

31.17 

43.96 

31.36 

43.82 

31 .55 

| 54 

55 

45.05 

31.55 

44.92 

31.74 

44.78 

131.94 

44.64 

32.13 

I 551 

56 

45.87 

32.12 

45.73 

32.32 

45.59 

32.52 

45.45 

32.72 

56 

57 

46.69 

32.69 

46.55 

32.90 

46.40 

(33.10 

46,26 

33.30 

| 57 

58 

47.51 

33.27 

47.37 

33.47 

47.22 

33.68 

| 47.07 

33.89 

j 58 

59 

48.33 

33.84 

48.18 

34.05 

48.03 

34.26 

47.88 

34.47 

I 59 

60 

49.15 

34.41 

49.00 

34.63 

48.85 

|34.84 

48.69 

35.05 

60 

61 

49.97 

34.99 

49.82 

35.21 

49.66 

I 35.42 

49.51 

35.64 

61 

62 

50.79 

35.56 

50.63 

35.78 

50.48 

!36.00 

50.32 

36.22 

1 62 

63 

51.61 

36.14 

51.45 

36.36 

51.29 

36.58 

51.13 

36.81 

63 

64 

52.43 

36.71 

52.27 

36.94 

52.10 

37.16 

51.94 

37.39 

i 64 

65 

53.24 

37.28 

53.08 

37.51 

52.92 

37.75 

52.75 

37.98 

65 

66 

54.06 

37.86 

53.90 

38.09 

53.73 

38.33 

53.56 

38.56 

1 66 

67 

54.88 

38.43 

54.71 

38.67 

54.55 

38.91 

54.38 

39.14 

! 67 

68 

55.70 

39.00 

55.53 

39.25 

55.36 

39.49 

55.19 

39.73 

; 68 

69 

56.52 

39.58 

56.35 

39.82 

56.17 

40.07 

56.00 

40.31 

! 69 

70 

57.34 

40.15 

57.16 

40 40 

56.99 

40.65 

56.81 

40.90 

70 

71 

58.16 

40.72 

57.98 

40.98 

157.80 

41.23 

57.62 

41.48 

71 

72 

58.98 

41.30 

53.80 

41.55 

! 58.62 

41.81 

58.43 

42.07 

72 

73 

59.80 

41.87 

59.61 

42.13 

159.43 

42.39 

59.24 

42.65 

73 

74 

60.62 

42.44 

60.43 

42.71 

60.24 

42.97 

60.06 

43.23 

74 

75 

61.44 

43.02 

61.25 

43.29 

61.06 

43.55 

60.87 

43.82 

75 

76 

62.26 

43.59 

62.06 

43.86 

61.87 

44.13 

61.68 

44.40 

76 

77 

63.07 

44.17 

62.88 

44.44 

j 62.69 

44.71 

62.49 

44.99 

77 

78 

63.89 

44.74 

63.70 

45.02 

63.50 

45.29 

63.30 

45.57 

78 

79 

64.71 

45.31 

64.51 

45.59 

64.32 

45.88 

64.11 

46.16 

79 

80 

65.53 

45.89 

65.33 

46.17 

65.13 

46.46 

64.93 | 

46.74 

80 

81 

66 .35 

46.46 

66.15 

46.75 

65.94 

47.04 

65.74 

47.32 

81 

82 

67.17 

47.03 

66.90 

47.33 

68.76 

47.62 

66.55 | 

47.91 

82 

83 

67.99 

47.61 

67.78 

47.90 

67.57 

48.20 

67.36 

48.49 

S3 

84 

68.81 

48.18 

68.60 

48.48 

68.39 

48.78 

68.17 

49.08 

84 

85 

69.63 

48.75 

69.41 

49.06 

69.20 

49.36 

68.98 

49.66 

85 

86 

70.45 

49.33 

70.23 

49.63 

70.01 

49.94 

69.80 

50.25 

86 

87 

71.27 

49.90 

71.05 

50.2 L 

70.83 

50.52 

70.61 

50.83 

87 

88 

72.09 

50.47 

71.86 

50.79 

71.64 

51.10 

71.42 ! 

51.41 

88 

89 

72.90 

51.05 

72.68 

51.37 

72.46 

51.68 

72.23 

52.00 

89 

90 

73.72 

51.62 

73.50 

51.94 

73.27 1 

52.26 1 

73.04 

52.58 

90 

91 

74.54 

52.20 

74.31 

52.52 

74.08 

52.84 

73.85 

.53.17 

91 

92 

75.36 

52.77 

75.13 

53.10 

74.90 

53.42 

74.66 

53.75 

92 

93 

76.18 

53.34 

75.95 

53.67 

75.71 

54.01 

75.48 

54.34 

93 

94 

77.00 

53.92 

76.76 

54.25 

76.53 

54.59 1 

76.29 

54.92 

94 

95 

77.82 

54.49 

77.58 

54.83 

77.34 

55.17 | 

77 10 

55.50 

95 

96 

78.64 

55.06 

78.40 

55.41 

78.16 

55.75 

77.91 

56.09 

96 

97 

79.46 

55.64 

79.21 

55.98 

78 97 

56.33 

78.72 

56.67 

97 

98 

SO. 28 

56.21 

80.03 

56.56 

79.78 

56.91 

79.53 

57.26 

98 

99 

81.10 

56.78 

80.85 

57.14 

80.60 

57.49 | 

80.35 

57.84 

99 

J 00 

81.92 

57.36 

81.66 

57.71 

81.41 

58.07 

81.16 

£8.42 

100 

® 

c 

G 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

© 

© 

c 

ci 

♦-> 

CO 

• 

55 Deg. 

54f Deg. 

54^ Deg. 

11 

1 

54^ Deg. 

» 

d 

oc 




















































































































74 


TRAVERSE TAKLE. 


Distance. 

36 Deg. 

36} Deg. 

36-g 

Deg. 

36} Deg. 

-1 

75* 

<r*- 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

s 

CD 

1 

0.81 

0.69 

0.81 

0.59 

0.80 

0.59 

0.80 

0.60 

1 

2 

1.62 

1.18 

1.61 

1.18 

1.61 

1.19 

1.60 

1 20 

9 

3 

2.43 

1.76 

2.42 

1.77 

2.41 

1.78 

2.40 

1.79 

3 

4 

3.24 

2.35 

3.23 

2.37 

3.22 

2.38 

3.20 

2.39 

4 

5 

4.05 

2.94 

4.03 

2.96 

4.02 

2.97] 

4.01 

2.99 

5 

6 

4.85 

3.53 

4.84 

3.55 

4.S2 

3.57 | 

4.81 

3.59 

6 

7 

5.66 

4.11 

5.65 

4.14 

5.63 

4.16 

5.61 

4.19 

7 

8 

6.47 

4.70 

6.45 

4.73 

6.43 

4.76 

6.41 

4.79 

8 

9 

7.28 

5.29 

7.26 

5.32 

7.23 

5.35 

7.21 

5.33 

9 

10 

8.09 

5.88 

8.06 

5 91 

8.04 

5.95 

8.01 

5.98 

10 

li 

8.90 

6.47 

8.87 

6.50 

8.84 

6.54 

8.81 

6.58 

11 

12 

9.71 

7.05 

9.68 

7.10 

9.65 

7.14 

9.61 

7.13 

12 

13 

10.52 

7.64 

10.48 

7.69 

10.45 

7.73 

10.42 

7.78 

13 

14 

11.33 

8.23 

11.29 

8.28 

11.25 

8.33 

11.22 

8.38 

14 

15 

12.14 

8.82 

12.10 

8.87 

12.06 

8.92 

12.02 

8.97 

15 

16 

12.94 

9.40 

12.90 

9.46 

12.86 

9.52 

12.82 

9.57 

16 

17 

13.75 

9.99 

13.71 

10.05 

13.67 

10.11 

13.62 

10. 17 

17 

18 

14.56 

10.58 

14.52 

10.64 

14.47 

30.71 

14.42 

10.77 

18 

19 

15.37 

11.17 

15.32 

11.23 

15.27 

11.30 j 

15.22 

11.37 

19 

20 

16.18 

11.76 

16.13 

11.83 

16.08 

11.90 

10.03 

11.97 

20 

21 

16.99 

12.34 

16.94 

12.42 

16.88 

12.49 

16.83 

12.56 

21 

OO 

/V V 

17.80 

12.93 

17.74 

13.01 

17.68 

13.09 1 

17.63 

13. 16 

22 

23 

18.61 

13.52 

18.55 

13.60 

18.49 

13.68 

18.43 

13.76 

23 

24 

19.42 

14.11 

19.35 

14.19 

19.29 

14.28 

19.23 

14.36 

24 

25 

20.23 

14.69 

20.16 

14.78 

20.10 

14.87 

20.03 

14.98 

25 

26 

21.03 

15.28 

20.97 

15.37 

20.90 

15.47 

20.83 

15.56 

26 

27 

21.84 

15.87 

21.77 

15.97 

21.70 

16.06 

21.63 

16.15 

27 

28 

22.65 

16.46 

22.58 

16.56 

22.51 

16.65 

22.44 

16.75 

28 

29 

23.46 

17.05 

23.39 

17.15 

23.31 

17.25i 

23.24 

17.35 

29 

30 

24.27 

17.63 

24.19 

17.74 

24.12 

17.84 

24.04 

17.95 

30 

31 

25.08 

18.22 

125.00 

18.33 

24.92 

18.41 

24.84 

18.55 

31 

32 

25.89 

18.SI 

125.81 

18.92 

25.72 

19.03 

25.64 

19.15 

32 

33 

26.70 

19.40 

26.61 

19.51 

26.53 

19.63 

26.44 

19.74 

33 

34 

27.51 

19.98 

27.42 

20.10 

27.33 

20.22 

27.24 

20.31 

34 

35 

28.32 

20.57 

|28.23 

20.70 

28.13 

20.82 

28.04 

20.94 

35 

36 

29.12 

21.16 

j 29.03 

21 .29 

28.94 

21.41 

28.85 

21.54 

36 

37 

29.93 

21.75 

29.84 

21.83 

29.74 

22.01 

29.65 

22.14 

37 

38 

30.74 

22.34 

30.64 

22.47 

30.55 

22.60 

30.45 

22.74 

38 

39 

31.55 

22.92 

31 .45 

23.06 

31.35 

23.20 

31.25 

23.33 

39 

40 

32.36 

23.51 

32.26 

23.65 

32.15 

23.79 

32.05 

23.93 

40 

41 

33.17 

24.10 

33.06 

24.24 

32.96 

24.39 

32.85 

24.53 

41 

42 

33.93 

24.69 

33.87 

24.83 

33.76 

24.98 

33.65 

25.13 

42 

43 

34.79 

25.27 

1 34.63 

25.43 

34.57 

25.58 

34.45 

25.73 

43 

44 

35.60 

25.86 

j35.48 

26.02 

35.37 

26.17 

35.26 

26.33 

44 

45 

36.41 

26.45 

36.29 

26.61 

36.17 

26.77 

j 36.06 

26.92 

15 

46 

37.21 

27.04 

137.10 

27.20 

36.98 

27.36 

36.86 

•27.52 

46 

47 

38.02 

27.63 

137.90 

27.79 

37.78 

27.96 

37.66 

23.12 

47 

48 

38.83 

28.21 

!38.71 

28.33 

38.59 

28.55 

33.46 

28.72 

48 

49 

39.64 

28.80 

39.52 

28.97 

39.39 

29.15 

39.26 

29.32 

49 

50 

40.45 

29.39 

40.32 

29.57 

40.19 

29.74 

40.06 

29.92 

50 

® 

V 

c 

Dap. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

oi 

o 

c 

rt 

w 

tfl 

) a 

54 Des. 

53} Deg. 

i 

53} Deg. 

53} Deg. 

ed 

•+-> 

CO 

• H 

Q 







































































































TRAVKKSE TABLE. 


5 


o 

• 

TO 

rf 

P 

36 Deg. 

36* Deg. 

36£ Deg. 

38| Deg. 

J 

O 

Vj 

I 

3 

O 

<5 


Dep. 

Lat. 

Dep. 

Lat 

Dep 

Lat. 

Dep. 

2 

51 

|41.26 

29.98 

41.13 

30.16 

41.00 

30.34 

40 86 

!30.51 

’ 51 

52 

42.07 

30.56 

41.94 

30.75 

41.80 

30.93 

41 67 

|31.11 

52 

53 

i42.88 

31 . 15 

42.74 

31.34 

42.60 

I 31.53 

42.47 

31.71 

53 

54 

|43.69 

31.74 

43.55 

31 .93 

:43.41 

1 32.12 

43.27 

32.31 

54 

55 

44.50 

32.33 

44.35 

32.52 

144.21 

;32.72 

!44.07 

32.91 

! 55 

56 

145.30 

32.92 

45.16 

33. 11 

145.02 

33.31 

144.87 

33.51 

i r 

5o 

57 

!46 . 11 

33.50 

45.97 

33.70 

1 45.82 

I 33.90 

145.67 

34.10 

57 

58 

!46.92 

34.09 

46.77 

34.30 

46.62 

! 34.50 

46.47 

34.70 

58 

59 

47.73 

34 . 68 

| 47.58 

34.89 

47.43 

35 09 

47.27 

35.30 

59 

GO 

48 . 54 

!35.27 

j 48,39 

35.48 

I 48 . 23 

35.69 

48.08 

35.90 

1 60 

61 

49.35 

35.85 

!49.19 

36.07 

49.04 

; 36 . 28 

48.88 

36.50 

61 

62 

50 . 16 

36.44 

50.00 

36 . 66 

49 . 84 

1 36.88 

49 . 68 

37.10 

62 

63 

150.97 

| 37 . 03 

; ! 50.81 

37.25 

50.64 

| 37.47 

50.48 

37.69 

63 

64 

!51.78 

37.62 

1 51.61 

37.84 

51.45 

38 . 07 

51.28 

38.29 

64 

65 

52.59 

38,21 

52.42 

38.44 

52.25 

38 . 66 

j 52.08 

38.89 

65 

66 

53 . 40 

38.79 

53.23 

39.03 

! 53 . 05 

39.26 

52.88 

39.49 

66 

67 

' 54.20 39.38 

54.03 

39.62 

53.86 

39.85 

!53.68 

40.09 

67 

68 

;55.01 

1 39.97 54.84 

40.21 

54.66 

40.45 

1 54.49 

40.69 

68 

69 

55.82 

I 40.56 

55.64 

40.80 

55.47 

41.04 

55 .'29 

41.28 

69 

70 

56.63 

! 41.14 

56.45 

41.39 

56.27 

41.64 

56.09 

41.88 

70 

71 

57.44 

i 41.73 

57.26 

41.98 

| 57.07 

42.23 

56.89 

42.48 

71 

72 

58.25 

j 42.32 

| 58.06 

42.57 

157.88 

42.83 

57.69 

43.08 

72 

73 

59.06 

142.91 

I 58.87 

43.17 

'58.68 

43.42 

58.49 

43.68 

73 

74 

59.87 

43.50 

59.68 

43.76 

59.49 

44 . 02 

59.29 

44.28 

74 

75 

60 . 68 

44.08 

60.48 

44.35 

60.29 

44.61 

60.09 

44.87 

75 

76 

61.49 

44.67 

61.29 

44.94 ! 

61.09 

45.21 

60.90 

45.47 

76 

77 

62.29 

45.26 

62.10 

45.53 

61.90 

45.80 

61.70 

40.07 

77 

78 

63.10 

45.85 

62.90 

46.12 

62.70 

46.40 

62.50 

46.67 

78 

79 

63.91 

46.43 

63.71 

46.71 

63.50 

46.99 

63.30 

47.27 

79 

80 

64.72 

47.02 

64.52 

47.30 

64.31 

47.59 j 

64.10 

47.87 

80 

81 

6 v) • 53 

47.61 

65.32 

47.90 

65.11 

48.18 

64.90 

48.46 

83 

82 

66.34 

48.20 

66.13 

48.49 

65.92 

48.78 

65.70 

49-06 

82 

83 

67.15 

48.79 

66.93 

49.08 

66.72 

49.37 

66.50 

49.66 

83 

84 

67.96 

49.37 j 

67.74 

49.67 

67.52 

49.97 

67.31 

50.26 

84 

85 

68.77 

49.961 

68.55 

50.26 

68.33 

50.56 

68.11 

50.86 

85 

86 

69.58 

50.55 

69.35 

50.85 

69.13 

51.15 

68.91 

51.46 

86 

87 

70.33 

51.14 

70.16 

51.44 

69.94 

51.75 

69.71 

52.05 

87 

88 

71.19 

51.73 

70.97 

52.04 

70.74 

52.34 

70.51 

52.65 

88 

89 

72.00 

52.31 

71.77 

52.63 

71.54 

52.94 

71.31 

53.25 

89 

90 

72.81 

52.90 ji 

72.58 

53.22 

72.35 

53.53 

72 . 11 

53.85 

90 

91 

73 . 62 

53.49 1 

73.39 

53.81 1 

73.15 

54.13 

72.91 

54.45 

91 

92 

74.43 

54.08 i 

74.19 

54.40 ! 

73.95 

54.72 

73.72 

55.05 

92 

S3 

75.24 

54.66 

75.00 

54.99 ! 

74.76 

55 , 32 

74.52 

55 . 64 

93 

94 

76.05 

55.25 

75 . 81 

55.58 

75.56 

55.91 

75.32 

56 . 24 

94 

95 

76.86 

55.84 

76.61 

56.17 

76.37 

56.51 

76.12 

56.84 

95 

96 j 

77.67 1 

56.43 i 

77.42 

56.77 

77.17 

57.10 

76 . 92 

57.44 

96 

97 ' 

78.4? 

57.02 j 

78 . 23 

57.36 

77.97 

57.70 

77 . 72 

58.04 

97 

98 1 

79.28 

57.60 

79 . 03 

57.95 

78 . 78 

58.29 

78.52 

58.64 

98 

99 

80.09 

58.19! 

79 . 84 

58.54 

79.58 

58.89 

79- 32 

59.23 

99 

100 , 

80.90 

58 . 78 j 

80.64 

59.13 

80.39 

59.48 

80.13 

59.83 

100 

« ! 
O ' 

c 

Dep. j 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

Lat. 

6 

V 

a 

aS 

w 

3 

54 Deg. 

1 

531 Deg. 

1 

53* Deg. 

53* Dog. 

IL 

s 

















































































































76 TRAVERSE TABLE. 


a 

37 Deg. 

37* Deg. 

37^ Deg. 

37f Deg. 

C 

S' 

P 

& 

5 

3 ° 

\ 9 









Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep 

*3 

O 

P 

i 1 

0,80 

0.60 

0.80 

0.61 

0.79 

0.61 

0.79 

0.61 


i 2 

1 .60 

1.20 

1.59 

1.21 

1.59 

1.22 

1.58 

1.22 

2 

3 

2.40 

1.81 

2.39 

1.82 

2.38 

1 .83 

2.37 

1.84 

3 

4 

3.19 

2.41 

3.18 

2.42 

3.17 

2.43 | 

3.16 

2.45 

4 

5 

3.99 

3.01 

3.98 

3.03 

3.97 

3.04 

3.95 

3.06 

5 

6 

4.79 

3.61 

4.78 

3.63 

4.76 

3.65 

4.74 

3.67 

6 

? 

5.59 

4.21 

5.57 

4.24 

5.55 

4.26 

5.53 

4.29 

7 

| 8 

6 .39 

4.81 

6.37 

4.84 

6.35 

4.87 

6.33 

4.90 

8 

9 

7.19 

5.42 

7.16 

5 45 

7.14 

5.48 | 

7.12 

5.51 

9 

10 

7.99 

6 .02] 

7.98 

6.05 

7.93 

6.09 | 

7.91 

6.12 

10 

TT 

8.78' 

6.62 | 

8.76 

6.66 

8.73 

6.70 ] 

8.70 

6.73 

11 

12 

9.58 

7.22 

9.55 

7.26 i 

9.52 

7.31 

9.49 

7.35 

12 

13 

10.38 

7.82 

10.35 

7.87 ! 10.31 

7.91 

10.28 

7.96 

13 

14 

11.18 

8.43 : 

11.14 

8.47 ! 
9.08 

11.11 

8.52 i 

11.07 

8.57 ! 

14 

IS 

11.98 

9.03 

11.94 

11.90 

9.13 

11.86 

9.18 

15 

16 

12.78 

9.63 

12.74 

9.68 

12.69 

9.74 

12.65 

9.80 

16 

17 

13.58 

10.23 

13.53 

10.29 

13.49 

10.35 1 

13.44 1 

10.41 

17 

18 

14.38 

10.83 

14.33 

10.90 

14.28 

10.96 

14.23 

11.02 

18 

19 

15.17 

11.43 

15.12 

11.50 

15.07 

11.57 

15.02 

11.63 

19 

20 

15.97 

12.04 

15.92 

12.11 

15.87 

12.18 ] 

15.81 | 

12.24 

20 

tv l 

16.77 

12.64 

16.72 

12.71 

16.66 

12.78 

13.60 

12.86 

21 

22 

17.57 

13.24 

17.51 

13.32 

17.45 

13.39 

17.40 

13.47 

22 

23 

18.37 

13.84 

18.31 

13.92 

18.25 

14.00 | 

18.19 

14.08 ! 

23 

24 

19.17 

14.44 

19.10 

14.53 

19.04 

14.61 

18.98 

14.69 ; 

24 

25 

19.97 

15.05 

19.90 

15.13 

19.83 

15.22 

19.77 

15,31 

25 

S 26 

20.76 

15.65 

20.70 

15.74 

20.63 

15.83 

20.56 

15.92 

26 

27 

21.56 

16.25 

21.49 

16.34 

21.42 

16.44 

21.35 

16.53 

27 

28 

22.38 

16.85 

22.29 

16.95 

22.21 

17.05 

22.14 

17.14 

28 

29 

23.16 

17.45 

23.08 

17.55 

23.01 

17.65 

22.93 

17.75 

29 

30 

23.96 

18.05 

23.88 

18.16 

23.8.0 

18.26 

23.72 

18.37 

30 

"31 

24.76 

18.66 

24.68 

18.76 

24.59 

18.87 ] 

24.51 

18.98 

31 

32 

25.56 

19.26 

25.47 

19.37 

25.39 

19.48 

25.30 

19.59 

32 

33 

20.35 

19.86 

26.27 

19.97 

26.18 

20.09 

26.00 

20.20 

33 

34 

27.15 

20.46 

27.06 

20,58 

26.97 

20.70 

26.88 

20.82 

34 

ii 35 

27.95 

21.06 

27.86 

21.19 

27.77 

21.31 

27.67 

21.43 

35 

36 

28.75 

21.67 

28.66 

21.79 

28.56 

21.92 

28.46 

22.04 

36 

37 

29.55 

22.27 

29.45 

22.40 

29.35 

22.52 

29.26 

22.65 

37 

38 

30.35 

22.87 

30.25 

23.00 

30.15 

23.13 

30.05 

23.26 

38 

\ 39 

31.15 

23.47 

31.04 

23.61 

30.94 

23.74 

30.84 

23.88 

39 

40 

31.95 

24.07 

31.84 

24.21 

31.73 

24.35 

31.63 

24.49 

40 

41 

32.74 

24.67 

32.04 

24.82 

32 53 

24.93 

32.42 

25.10 

41 

42 

33.54 

25.28 

33.43 

125.42 

33 32 

25.57 

33.21 

j 25.71 

42 

43 

34.34 

25.88 

34.23 

26.03 

34.11 

26.18 

34.00 

1 26.33 

43 

44 

35.14 

20.48 

35.02 

26.63 

34.91 

26.79 

34.79 

26.94 

44 

45 

35.94 

27.08 

35.82 

27.24 

35.70 

27.39 

35.58 

27.55 

45 

40 

36.74 

27.68 

36.02 

27.84 

36.49 

1 28.00 

36.37 

28.16 

46 

47 

37.54 

28.29 

37.41 

28.45 

37.29 

] 28.61 

37.16 

28.77 

47 

48 

38.33 

28.89 

38.21 

29.05 

38.08 

29.22 

37.95 

29.39 

48 

49 

39.13 

29.49 

39.00 

29.66 

38.87 

29.83 

38.74 

30.00 

49 

50 

39.93 

30.09 

39.80 

30.26 

39.67 

30.44 

39.53 

30.61 

50 

6 

o 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

*—* 

; ri 

TQ 

“S 

53 Deg. 

52| Deg. 

52J Deg 

52J Deg. 

<1 

ci 

.2 

Q 

















































































































KAVKKSE TAHI.E. 


7 ? 


Distance, j 

37 Deg. 

37* Deg. 

37£ Deg. 

37* Deg. 

5 

! 5T 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

P 

o 

CD 

51 

40.73 

30.69 

40.60 

30.87 

40.46 

31.05 

40.33 

31.22 

~51 

52 

41.53 

31.29 

41.39 

31.48 

41.25 

31.66 

41.12 

31.84 

52 1 

53 

42.33 

31.90 

42.19 

32.08 

42.05 

32.26 

41.91 

32.45 

53 1 

54 

43.13 

32.50 

42.98 

32.69 

42.84 

32.87 

42.70 

33.06 

54 j 

55 

43.92 

33.10 

43.78 

33.29 

43.63 

33.48 

43.49 

33.67 

55 J 

56 

44.72 

33.70 

44.58 

33.90 

44.43 

34.09 

44.28 

34.28 

56 j 

57 

45.52 

34.30 

45.37 

34.50 

45.22 

34.70 

45.07 

34.90 

57 

58 

46.32 

i 34.91 

46.17 

35.11 

46.01 

35.31 

45.86 

35.51 

58 

59 

47.12 

1 35.51 

46.96 

35.71 

46.81 

35.92 

46.65 

36.12 

59 

60 

47.92 

36.11 

47.76 

36.32 

47.60 

36.53 

47.44 

36.73 

60 

61 

48.72 

36.71 

48.56 

36.92 

1 48.39 

37.13 

48.23 

37.35 

61 

62 

49.52 

37.31 

49.35 

37.53 

49.19 

37.74 

49.02 

37.96 

62 

63 

50.31 

37.91 

50.15 

38.13 

49i98 

38.35 

49.81 

38.57 

63 

64 

51.11 

38.52 

50.94 

38.74 

50.77 

38.96 

50.60 

39.18 

64 

65 

51.91 

39.12 

51.74 

39.34 

51.57 

39.57 

51.39 

39.79 

65 

66 

52.71 

39.72 

52.54 

39.95 

52.36 

40.18 

52.19 

40.41 

66 

67 

53.51 

40.32 

53.33 

40.55 

53.15 

40.79 

52.98 

41.02 

67 

68 

54.31 

40.92 

54.13 

41.16 

53.95 

41.40 

53.77 

41.63 

68 

69 

55.11 

41.53 

54.92 

41.77 

54.74 

42.00 

54.56 

42.24 

6» 

70 

05.90 

42.13 

55.72 

42.37 

55.53 

42.61 

55.35 

42.86 

70 

71 

56.70 

42.73 

56.52 

42.98 

56.33 

43.22 

56.14 

43.47 

71 

72 

57.50 

43.33 

57.31 

43.58 

57.12 

43.83 

56.93 

44.08 

72 

73 

58.30 

43.93 

58.11 

44.19 

57.91 

44.44 

57.72 

44.69 

73 

74 

59.10 

44.53 

58.90 

44.79 

58.71 

45.05 

58.51 

45.30 

74 

75 

59.90 

45.14 

59.70 

45.40 

59.50 

45.66 

59.30 

45.92 

75 

76 

60.70 

45.74 

60.50 

46.00 

60.29 

46.27 

60.09 

46.53 

76 

77 

61.49 

46.34 

61.29 

46.61 

61.09 

46.87 

60.88 

47.14 

77 

78 

62.29 

46.94 

62.09 

47.21 

61.88 

47.48 

61.67 

47.75 

78 

79 

63.09 

47.54 

62.83 

47.82 

62.67 

48.09 

62.46 

48.37 

79 

80 

63.89 

48.15 

63.68 

48.42 

63.47 

48.70 

63.26 

48.98 

80 

81 

64.69 

48.75 

64.48 

49.03 

64.26 

49.31 

64.05 

49.59 

81 

82 

65.49 

49.35 

65.27 

49.63 

65.05 

49.92 

64.84 

50.20 

82 

83 

66.29 

49.95 

66.07 

50.24 

65.85 

5.0.53 

65.63 

50.81 

83 

84 

67.09 

50.55 

66.86 

50.84 

66.64 

51.14 

66.42 

51.43 

84 

85 

67.88 

51.15 

67.66 

51.45 

67.43 

51.74 

67.21 

52.04 

85 

86 

68.68 

51.76 

68.46 

52.06 

68.23 

52.35 

68.00 

52.65 

86 

87 

69.48 

52.36 

69.25 

52.66 

69.02 

52.96 

68 .79 

53.26 

87 

88 

70.28 

52.96 

70.05 

53.27 

69.82 

53.57 

69.58 

53.88 

88 

89 

71.08 

53.56 

70.84 

53.87 

70.61 

54.18 

70.37 

54.49 

89 

90 

71.8S 

54.16 

71.64 

54.48 

71.40 

54.79 

71.16 

55.10 

90 

91 

72.68 j 

54.77 

72.44 

55.08 

72.20 

55.40 

71.95 

55.71 

91 

92 

73.47 

55.37 

73.23 

55.69 

72.99 

56.01 

72.74 

56.32 

92 

93 

74.27 

55.97 

74.03 

56.29 

73.78 

56.61 

73.53 

56.94 

931 

94 

75.07 

56.57 

74.82 

56.90 

74.58 

57.22 

74.32 

57.55 

94 | 

95 

75.87 

57.17 

75.62 

57.50 

75.37 

57.83 

75.12 

58.16 

95 I 

96 

76.67 

57.77 

76.42 

58.11 

76.16 

58.44 

75 91 

58.77 

96 

97 

77.47 

58.33 

77.21 

58.71 

76.96 

59.05 

76 70 

59.39 

97 

98 

78.27 

58,98 

78.01 

59.32 

77.75 

59.66 

77.49 

60.00 

98 

99 

79.06 

59.58 

78.80 

59.92 

78.54 

60.27 

78.28 

60.61 

99 

100 

79.86 

60.18 

79.60 

60.53 

79.34 

60.88 

79.07 

61.22 

! 00 

6 

8 1 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dcd. 

A 

Lat. 

o’ 

o 

a 

ci | 
«-* 

V) 

• r-H 

a 

53 Deg. 

52| Deg. 

52£ Deg. 

52* Deg. 

cd 

os 

a 


24 










































































































78 


TRAVERSE TABLE 


| Distance. 

38 Dog. 

38.1 Deg. 

38^ Deg. 

38f 

Deg. 

| 

O ' 

<—► 

C3 

b 

n 

? 

Lai. 

Dep. 

Lat. 

Dep. 

Lilt. 

Dep. 

Lat. 

Dep. 

J 1 

0 . 

79 i 

0 . 

62 

0.79 

0.62 

0.78 

0.62 

0 . 

78 

0 63 

i 

] 2 

1 . 

58; 

1 . 

23 

1.57 

1.24 

1.57 

1.24 

1 . 

56 

1.25 

o 

4 

J 3 I 

2 . 

36 

1 . 

85 

2.36 

1.86 

2.35 

1.87 

2 . 

34 

1.88 

3 

1 4 

3. 

15 

2 . 

46 

3.14 

2.4S 

3.13 

2.49 

3. 

12 

2.50 

4 

5 

3. 

94 

3. 

08 

3.93 

3.10 

3.91 

3 11 

3. 

90 

3.13 

5 

6 

4. 

73 

3. 

69 

4.71 | 

3.71 

4.70 

3.74 

4. 

68 

3.76 

j 

7 

5. 

52 

4. 

31 

5.50 I 

4.33 

5.48 

4.36 

5. 

46 

4.38 

7 

8 

6 . 

30 

4. 

93 

6.28 

4.95 

6.26 

4.98 

6 . 

24 

5.01 

9 

9 

7. 

09 

5. 

54 

7.07 

5.57 

7.04 

5.60 

7. 

02 

5.63 

9 

10 

7. 

88 ; 

6 . 

16 

7.85 

6.19 

7.83 j 

6.23 

7. 

80 

6.26 

10 

11 

8 . 

67 

6 . 

77 

8.64 

6.81' 

8.61 

6.85 

8 . 

58 

6.89 

11 

12 

9. 

46 

7. 

39 

9.42 

7.43 

9.39 j 

7.47 1 

9. 

36 

7.51 

12 

13 

10 . 

24 

8 . 

00 

10.21 

8.05 

10.17 

8.09 

10 . 

14 

8.14 

13 

14 

11 . 

03 

8 . 

62 

10.99 

8.67 

10.96 

8.72 

10 . 

92 

8.76 

14 

15 

11 

82 

9. 

23 

11.78 

9.29 

11.74 

9.34 

11 . 

70 

9.39 

15 

16 

12 . 

61 

9. 

85 

12.57 

9.91 

12.52 

9.96 

12 . 

48 

10.61 

16 

17 

13. 

40 

10 . 

47 ! 

13.35 

10.52 

13.30 

10.58 

13. 

26 

10.64 

17 

18 

14. 

18 

11 . 

08 | 

14.14 

11.14 

14.09 

11.21 

14. 

04 

11 .27 

18 

19 

14. 

97 

11 

70 | 

14.92 

11.76 

14.87 

11.83 

14. 

82 

11.89 

19 

20 

15. 

76 

12 . 

31 | 

15.71 

12.38 

15.65 

12.45 

15. 

60 

12.52 

20 

21 

16. 

55 

12 . 

93 

16.49 

13.00 

16.43 

13.07 I 

16 

38 

13.14 

21 

99 

17. 

34 

13. 

54 

17.28 

13.62 

17.22 

13.70 

17 

16 

13.77 

22 

23 

13. 

12 

14. 

16 

18.06 

14.24 

18.00 

14.32 

17 

94 

14.40 

23 

24 

18. 

91 

14. 

78 j 

18.85 

14.86 

18.78 

14.94 

18 

72 

15.02 

24 

25 

19. 

70 

15. 

39 ! 

19.63 

15.48 

19.57 

15.56 

' 19 

50 

15.65 

25 

26 

20 . 

49 

16 

01 

20.42 

16.10 

20.35 

16.19 

20 

28 

16.27 

26 

27 

21 . 

28 

16 

62 

21.20 

16.72 

21.13 

16.8) 

21 

06 

16.90 

27 

23 

22 . 

06 

17 

24 

21.99 

17.33 

21.91 

17.43 

21 

84 

17.53 

28 

29 

22 

85 

17 

85 

22.77 

17.95 

22.70 

18.05 

22 

.62 

18.15 

29 

30 

23 

64 

18 

47 

23.56 

18.57 

23.48 

18.63 

23 

.40 

18.78 

30 


24 

13 

19 

09 

24.3 4 

19.19 

24.26 

19.30 

24 

IS 

19.40 

31 

32 

25 

22 

19 

.70 

25.13 

19.81 

25.04 

19.92 

24 

.96 

20.03 

32 

1 33 

26 

00 

20 

.32 

25.92 

20.43 

25.83 

20.54 

25 

.74 

; 20.66 

! 33 

34 

26 

.79 

20 

.93 

26.70 

21.05 

26.61 

21.17 

26 

.52 

:21.28 

34 

35 

27 

.58 

21 

.55 

127.49 

21.67 

27.39 

21.79 

27 

.30 

121.91 

35 

36 

*>Q 

.37 

22 

16 

128.27 

22.29 

28.17 

22.41 

; 28 

.08 

22.53 

36 

37 

29 

16 

22 

.78 

29.06 

! 22.91 

28.96 

23.03 

28 

.86 

23.16 

; 37 

38 

29 

.94 

23 

.40 

29.84 

|23.53 

29.74 

23.66 

: 29 

.64 

23.79 

33 

39 

30 

.73 

24 

.01 

30.63 

24.14 

30.52 

1 24.23 

I 30 

.42 

24.41 

i 39 

40 

31 

.52 

24 

.63 

81.41 

!24.76 

31.30 

! 24.90 

31 

.20 

| 25.04 

40 

41 

32 

.31 

25 

. 24 

32.20 

25.3S 

32.09 

25.52 

31 

. 98 

j 25.66 

: 41 

42 

33 

.10 

25 

.86 

32.98 

26.00 

32.87 

|26.15 

32 

. 76 

26.29 

42 

43 

33 

.88 

26 

.47 

33.77 

26.62 

33.65 

i 26.77 

33 

.53 

26.91 

! 43 

44 

34 

.67 1 27 

.09 

34.55 

27.24 

34.4? 

| 27.39 

34 

.31 

27.54 

44 

45 

35 

46 

I 27 

.70 

35.34 

27 .86 

35.22 

' 28.01 

1 35 

-09 

28.17 

45 

1 40 

36 

.25 

1 28 

.32 

36.12 

' 28.48 

36.00 

28.64 

jj 35 

.87 

28.79 

46 

47 

37 

.04 

28 

.94 

36.91 

29.10 

36.78 

23 26 

36 

.65 

! 29.42 

47 

48 

37 

.82 

29 

. 55 

37.70 

29.72 

1 37.57 

29.83 

; 37 

43 

30.04 

48 

19 

38 

.61 

30 

. 17 

38.48 

i 30.34 

38.35 

30.50 

1 33 

.21 

! 30.67 

49 

50 

39 

.40 

1 30 

.78 

39.27 

30.95 

39.13 

1 31 IS 

30 

.99 

31.30 

50 

6 

o 

a 

d 

■+-> 

CC 

• rH 

1 3 

Dep. 

1 Lut. 

Dep. 

Lat. 

Dep. 

L<a, 

v ! 

y 

" i 

Lat. 

1 

I § 


52 Deg 

• 

5 If Deg. 

51^ Deg. 

5If Dog. 

! 

! - 

C/3 

1 •’-« 

S Q 










































































































TRAVERSE TARI E. 


79 


Distance.) 

38 Deg. 

33$ Deg. 

i 

38$ Deg. 

3-31 Deg. 

i W 

PT 

<-► 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

1 T'W 

i Dep. 

Lat, 

Dep. 

-j 3 

i 3 

51 

40.19 

31.40 

40.05 

31.57 

39.91 

31.75 

39.77 

31 .92 

1 51 « 

52 

40.98 

32.01 

40.84 

32.19 

40.70 

32.37 

40.55 

32.55 

1 52 

53 

41.76 

132.63 

41.62 

32.81 

41.48 

I32.99 

41.33 

33.17 

53 1 

54 

42.55 

33.25 

42.41 

33.43 

42.26 

33.62 

42.11 

33.89 

54 

55 

43.34 

33.86 

43.19 

;34.05 

43.04 

34.24 

42.89 

34.43 

55 

56 

44.13 

34.48 

43.98 

34.67 

43.83 

134.86 

43.67 

35.05 

56 

57 

44.92 

35.09 

44.76 

35.29 

44.61 

|35.48 

44.45 

35.68 

57 

58 

45.70 

35.71 

45.55 

35.91 

45.39 

36.11 

45.23 

36.30 

53 

59 

46.49 

36.32 

46.33 

36.53 

46.17 

136.73 

46.01 

36.93 

59 

60 

47.28 

36.94 

! 47.12 

37.15 

46.96 

137.35 

46.79 

37.56 

. 60 

61 

48.07 

37.56 

47.90 

37.76 

47.74 

37.97 

47.57 

1 38.18 

i 61 

62 

48.86 

38.17 

48.69 

38.38 

48.52 

38.60 

48.35 

i38.81 

62 

63 

49.64 

38.79 

49.47 

39.00 

49.30 

39.22 

49.13 

• 09.43 

! 63 

64 

50.43 

39.40 

50.26 

39.62 

!50.09 

39.84 

49.91 

40.06 

! 64 

65 

51.22 

40.02 

51.05 

40.24 

50.87 

40.46 

50.69 

10.08 

, 65 

66 

52.01 

40.63 

51.83 

40.86 

51.65 

41.09 

51.47 

41.31 

66 

67 

52.80 

41.25 

52.62 

41.48 

52.43 

41.71 

52.25 

41.94 

67 

68 

53.58 

41.86 

53.40 

42.10 

j 53.22 

42.33 

i 53.03 

42.55 

63 

69 

54.37 

42.48 

54.19 

42.72 

|54.00 

42.95 

53.81 

43.19 

69 

70 

55.16 

43.10 

54.97 

43.34 

54.78 

43.58 

f54.59 

43.81 

70 

71 

55.95 

43.71 

55.76 

43.96 

55.57 

44.20 

1 55.37 

44 44 1 71 

72 

56.74 

44.33 

56.54 

44.57 

56.35 

44.82 

156.15 

45 07 

t 2 

73 

57.52 

44.94 

j 57.33 

45.19 

57.13 

45.44 

j 56.93 

45.69 

! 73 

74 

58.31 

45.56 

58.11 

45.81 

57.91 

46.07 

57.71 

46.32 

74 

75 

59.10 

46.17 

58.90 

46.43 

58.70 

46.69 

58.49 

46.94 | 75 

76 

59.89 

46.79 

59.68 

47.05 

59.48 

47.31 

59.27 

47.57 

76 

77 

60.68 

47.41 

60.47 

47.67 

60.26 

47.93 

60 05 

48.20 

77 

/8 

61.46 

48.02 

61.25 

48.29 

61.04 

48.56 

60 83 

48.82 

■ 78 

79 

62.25 

48.64 

62.04 

48.91 

61.83 

49.18 

61.61 

49.45 

79 

| 80 

63.04 

49.25 

62.83 

49.53 

62.61 

49.80 

62.39 

50.07 

j 80 

I Si 

63.83 

49.87 

63.61 

50.15 

63.39 

50.42 

63.17 

50.70 

i 

1 $ 2 

64.62 

50.48 

64.40 

50.77 

64.17 

51.05 

63.95 

51.33 

: 82 

83 

65.40 

51.10 

65.18 

51.38 1 

64.96 

51.67 

64.73 

51.95 

83 

84 

66.19 

51.72 

65.97 

52.00 

65.74 

52.29 

65.51 

52.58 

84 

85 

66.98 

52.33 

66.75 

52.62 

66.52 

52.91 

66.29 

53.20 

85 

86 

67.77 

52.95 

67.54 

53.34 

67.30 

53.54 

67.0? 

53.83 

86 

87 

68.56 

53.56 

68.32 

53.86 I 

68.09 

54.16 

67.85 

54.46 

87 

83 

69.34 

54.18 

69.11 

54.48 | 

68.87 

54.78 

68.63 

55.08 

88 

89 

70.13 

54.79 

69.89 

55.10 If 

69.65 

55.40 

69.41 

55.7! 

89 

90 

70.92 

55.41 

70.68 

55.72 j 

70.43 

56.03 

70.19 

56.33 

90 

91 

71.71 

56.03 

71.46 

56.34 

71.22 

56.65 

70.97 

£6.96 

91 

92 

72.50 

56.64 

72.25 

56.96 

72.00 

57.27 

71.75 

67.58 

92 

93 

73.28 

57.26 

73.03 

57.58 

72.78 

57,89 

72.53 

53.21 

93 

94 

74.07 

57.87 

73.82 

58.19 

73.57 

58.52 ! 

73.31 

53.84 

94 

95 

74 .86 

58.49 

74.61 

58.81 

74.35 

59.14 1 

74.09 

59.46 

95 

96 

75.65 

59.10 

75.39 

59.43 

75.13 

59.76 

74.87 

60 09 

96 

97 

76.44 

59.72 

76.18 

60.05 

75.91 

60.38 

75.65 

60 71 

97 

93 

77.22 

6U.33 

76.96 

60.67 

76.70 

61.01 

76.43 

61.34 

98 

99 

78,01 

60.95 

77.75 

61.29 

77.48 

61.63 

77.21 

61.97 

99 

100 

78.80 

61.57 

78.53 

61.91 

78.26 

62.25 

77.99 

62.59 

109 

J 

Distance.j 

f 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. | 

Dep. 

Lat. 

j Distance.] 

52 Deg. 

51 $ Dog. 

1 

51 \ Deg. 

i| 

1 

5U Deg 










































































































































80 


TRAVKltSi: TAHLE. 


o 

X 

r-*- 

39 Deg. 

39.| Deg. 

391 

Deg. 

39,f Deg. 

Dista 

3 

3 

A 

Liit. 

1 Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

O 

re 

I 

0.78 

0.63 

0.77 

0.63" 

0.77 

0.64 

0.77 

0.64 

1 

2 

1.55 

1.26 

1.55 

1.27 

1.54 

1.27 

1.54 

1.28 

o 

** 

3 

2.33 

1.89 

2.32 

1.90 

2.31 

1.91 

2.31 

1.92 

3 

4 

3.11 

2.52 

3.10 

2.53 

3.09 

2.54 

3.08 

2.56 

4 

5 

3.89 

3.15 

3.87 

3.16 

3.86 

3.18 

3.84 

3.20 

5 

8 

4.60 

3.78 

4.65 

3.80 

4.53 

3.82 

4.61 

3.84 

6 

7 

5.44 

4.41 

5.42 

4.43 

5.40 

4.45 

5.38 

4.48 

7 

8 

6.22 

5.03 

6.20 

5.00 

6.17 

5.09 

6.15 

5.12 

8 

9 

6.99 

5.66 

6.97 

5.69 

6.94 

5.72 

6.92 

5.75 

9 

10 

7.77 

6.29 

7.74 

6.33 

7.72 

6.36 

7.69 

6.39 

10 

li 

8.55 

6.92 

8.52 

6.96 

8.49 

7.00 

8.46 

7.03 

11 

13 

9.33 

7.55 

9.29 

7.59 

9.26 

7.63 

9.23 

7.67 

12 

13 

10. 10 

8.18 

10.07 

8.23 

10.03 

8.27 

9.99 

8.31 

13 

14 

10.88 

8.81 

10.84 

8.86 

10.80 

8.91 

10.76 

8.95 

14 

15 

11.66 

9.44 

11.62 

9.49 

11.57 

9.54 

11.53 

9.59 

15 

16 

12.43 

10.07 

12.39 

10.12 

12.35 

10.18 

12.30 

10.23 

16 

17 

13.21 

10.70 

13.16 

10.76 

13.12 

10.81 

13.07 

10.87 

17 

18 

13.99 

11.33 

13.94 

11.39 

13.89 

11.45 

13.84 

11.51 

18 

19 

14.77 

11.96 

14.71 

12.02 

14 66 

12.09 

14.61 

12.15 

19 

20 

15.54 

12.59 

15.49 

12.65 

15.43 

12.72 

15.38 

12.79 

20 

21 

16.32 

13.22 

16.26 

13.29 

16.20 

13.36 

16.15 

13.43 

21 

22 

17.10 

13.84 

17.04 

13.92 

16.98 

13.99 1 

16.91 

14.07 

22 

23 

17.87 

14.47 

17.81 

14.55 

17.75 

14.63 

17.68 

14.71 

23 

24 

18.65 

15.10 

18.59 

15.18 

18.52 

15.27 

18.45 

15.35 

24 

25 

19.43 

15.73 

19.36 

15.82 

19.29 

15.90 

19.22 

15.99 

25 

26 

20.21 

16.36 

20.13 

16.45 

20.06 

16.54 

19.99 

16.63 

26 

27 

20.98 

16.99 

20.91 

17.08 

20.83 

17.17 

20.76 

17.26 

27 

28 

21.76 

17.62 

21.68 

17.72 

21.61 

17.81 

21.53 

17.90 

28 

29 

22.54 

18.25 

22.46 

18.35 

22.38 

18.45 

22.30 

18.54 

29 

30 

23.31 

18.88 

23.23 

18.98 

23.15 

19.08 

23.07 

19.18 

30 

31 

24.09 

19.51 

24.01 

19.61 

23.92 

19.72 

23.83 

19.82 

31 

32 

24.87 

20.14 

24.78 

20.25 

24.69 

20.35 

24.60 

20.46 

32 

33 

25.65 

20.77 

25.55 

20.88 

25.46 

20.99 

25.37 

21.10 

33 

34 

26.42 

21.40 

26.33 

21.51 

26.24 

21.63 

26.14 

21.74 

34 

35 

27.20 

22.03 

27.10 

22.14 

27.01 

22.26 

26.91 

22.38 

35 

36 

27.98 

22.66 

27.88 

22.78 

27.78 

22.90 

27.68 

23.02 

3j5 

37 

28.75 

23.23 

28.65 

23.41 

28.55 

23.53 

28.45 

23.66 

37 

38 

29.53 

23.91 

29.43 

24.04 

29.32 

24.17 

29.22 

24.30 

38 

39 

30.31 

24.54 

30.20 

24.68 

30.09 

24.81 

29.98 

24.94 

39 

40 

31.09 

25.17 

30.98 

25.31 

30.86 

25.44 

30.75 

25.58 

40 

41 

31.86 

25.80 

31.75 

25.94 

31.64 

26.08 

31.52 

26.22 

41 

42 

32.64 

26.43 

32.52 

26.57 

32.41 

26.72 

32.29 

26.86 

42 

43 

33.42 

27.06 

33.30 

27.21 

33.18 

27.35 

33.06 

27.50 

43 

44 

34.19 

27.69 

34.07 

27.84 

33.95 

27.99 

33.83 

28.14 

44 

45 j 

34.97 

28.32 | 

34.85 

28.47 

34.72 

28.62 

34.60 

28.77 

45 

46 

35.75 

28.95 

35.62 

29.10 

35.49 

29.26 

35.37 

29.41 

46 

47 

36.53 

29.58 

36.40 

29.74 

36.27 

29.90 

36.14 

30.05 

47 

48 

37.30 

30.21 

37.17 

30.37 

37.04 

30.53 

36.90 

30.69 

48 

49 

38.08 

30.84 

37.95 

31.00 

37.81 

31.17 

37.67 

31.33 

49 

50 

38.86 

31.47 

38.72 

31.64 

38.58 

31.80 

38.44 

31.97 

50 

si 

o 

s 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

si 

u 

£ 

l/l 

Q 

51 Deg. 

50f Deg. 

50i Deg. 

50\ Deg. 

cd 

+* 

cn 

• 

Q 



















































































































TRAVERSE TABLE. 


81 


o 
>—• 

CD 

r**- 

P5 

39 Deg. 

| 

39i Deg. 

39i Deg. 

39J Deg. 

C 

• 

l/i 

e-+“ 

3 

o 

(D 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

S3 

o 

CD 

51 

39.63 

32.10 

39.49 

32.27 

39.35 

32.44 

39.21 

32.61 

51 

52 

40.41 

32.72 

40.27 

32.90 

40.12 

33.08 

39.98 

33. 25 

52 

53 

41.19 

33.35 

41.04 

i 33.53 

40.90 

33.71 

40.75 

33 89 

53 

64 

41.97 

33.98 

41.82 

j34.17 

41.67 

34.35 

41.52 

34.53 

54 

55 

42.74 

1 34 61 

I, 42.59 

i 34.80 

42.44 

34.98 

42.29 

35.17 

55 

56 

,43.52 

I 35.24 

j 43.37 

35.43 

43.21 

35.62 

43.06 

35.81 

56 

57 

144.30 

35.87 

I 44.14 

36.06 

43.98 

36.26 

43.82 

36.45 

57 

58 

45.07 

36.50 

44.91 

36.70 

44.75 

36.89 

44.59 

37.09 

58 

59 

45.85 

37.13 

45.69 

37.33 

45.53 

37.53 

45.36 

37.73 

59 

60 

46.63 

37.76 

46.46 

37.96 

46.30 

38.16 

46.13 

38.37 

60 

61 

47.41 

38.39 

47.24 

38.60 

47.07 

38.80 

46.90 

39.01 

61 

62 

48.18 

39.02 

48.01 

39.23 

47.84 

39.44 

47.67 

39.65 

62 

63 

48.96 

39.65 

48.79 

39.86 

48.61 

40.07 

48.44 

40.28 

63 

64 

49.74 

40.28 

49.56 

40.49 

49.38 

40.71 

49.21 

40.92 

64 

65 

50.51 

40.91 

50.34 

41.13 

50.16 

41.35 

49.97 

41.56 

65 

66 

51.29 

41.54 

51.11 

41.76 

50.93 

41.98 

50.74 

42.20 

66 

67 

52.07 

42.16 

51.88 

42.39 

51.70 

42.62 

51.51 

42.84 

67 

68 

52.85 

42.79 

52.66 

43.02 

52.47 

43.25 

52.28 

43.48 

68 

60 

53.52 

43.42 

53.43 

43.66 

53.24 

43.89 

53.05 

44.12 

69 

70 

54.40 

44.05 

54.21 

44.29 

54.01 

44.53 

53.82 

44.76 

70 

71 

55.18 

44.68 

54.98 

44.92 

54.79 

45.16 

54.59 

45.40 

71 

72 

55.95 

45.31 

55.76 

45.55 

55.56 

45.80 

55.36 

46.04 

72 

73 

56.73 

45.94 

56.53 

46.19 

56.33 

46.43 

56.13 

46.68 

73 

74 

57.51 

46.57 

57.31 

46.82 

57.10 

47.07 

56.89 

47.32 

74 

75 

58.29 

47.20 

58.08 

47.45 

57.87 

47.71 

57.66 

47.96 

75 

76 

59.06 

47.83 

58.85 

48.09 

58.64 

48.34 

58.43 

48.60 

76 

77 

59.84 

48.46 

59.63 

48.72 

59.42 

48.98 

59.20 

49.24 

77 

78 

60.62 

49.09 

60.40 

49.35 

60.19 

49.61 

59.97 

49.88 

78 

79 

61.39 

49.72 

61.18 

49.98 

60.96 

50.25 

60.74 

50 . 52 

79 

80 

62.17 

50 . 35 

61.95 

50.62 

61.73 

50.89 

61.51 

51.16 

80 

81 

62.95 

50.97 

62.73 

51.25 

62.50 

51.52 

62.28 

51.79 

81 

82 

63.73 

51 .60 

63.50 

51.88 

63.27 

52.16 

63.04 

52.43 

82 

83 

64.50 

52.23 

64.27 

52.51 

64.04 

52.79 

63.81 

53.07 

83 

84 

65.28 

52.86 

65.05 

53.15 

64.82 

53.43 

64.58 

53.71 

84 

85 

66.06 

53.49 

65.82 

53.78 

65.59 

54.07 

65.35 

54.35 

85 

86 

66.83 

54.12 

66 . 60 

54.41 

66.36 

54.70 

66.12 

54.99 

86 

87 

67.61 

54.75 

67.37 

55.05 

67.13 

55 . 34 

66.89 

55.63 

87 

88 

68.39 

55.38 

68.15 

55 . 68 

67.90 

55.97 

67.66 

56.27 

88 

89 

69.17 

56.01 

68.92 

56.32 

68.67 

56.61 

i68.43 

56.91 

89 

90 

69.94 

56.64 1 

69.70 

56.94 

69.45 

57.25 

69.20 

57.55 

90 

91 

70.72 

57.27 j 

70.47 

57.58 

70.22 

57.88 

69.96 

58.19 

91 

92 

71.50 

57.90 

71.24 

58.21 

70.99 

58.52 

70.73 

58.83 

92 

93 

72.27 

58.53 

72.02 

58.84 I 

71.76 

59.16 

71.50 

59.47 

93 

94 

73.05 

59.16 

72.79 , 

59.47 

72.53 

59.79 

72.27 

60.11 

94 

95 1 

73.83 

59.79 

73.57 

60.11 

73.30 

60.43 

73.04 

60.75 

95 

96 j 

74.01 

60.41 

74.34 

60.74 

74.08 

61.06 

73.81 

61.39 

96 

97 

75.38 

61.04 

75.12 

61.37 

74.85 , 

61.70 

74.58 

62.03 

9? 

98 

76.16 

61.67 

75.89 

62.01 

75.62 

62.34 

75.35 

62.66 

98 

99 

76.94 

62.30 

76.66 

62.64 

76.39 

62.97 

76.12 

63.30 

99 

100 

77.71 

62.93 

77.44 

63.27 

77.16 

63.61 

76.88 

63.91 

100 

© 

© 

c 

Dep. 

Lat. | 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

V 

c 

V. 

a 

c3 

.2 | 

r 

51 Deg. 

50f Deg- 

, 

50^ Deg. 

50| Deg. 

























































































































82 


TRAVERSE TABLE 


Distance. 

40 Deg. 

40} Deg. 

40i Deg 


40 k 

Deg. 

Distance. 


Dep. 

Lat. 

i 

Dep. 

Lat. 

Dep. 

Lat. 

Dep.. 

1 

0.77 

0.64 

0.76 

0.65 

0.76 

0. 

65 

0.76 

0.65 

1 

2 

1.53 

1.29 

1.53 

1.29 

1.52 

1. 

30 

1.52 

1.31 

2 

3 

2.30 

1.93 

2.29 

1.94 

2.28 

1. 

95 

2.27 

1.96 

3 

4 

3.06 

2.57 

3.05 

2.58 

3.04 

2. 

60 

3.03 

2.61 

4 

5 

3.83 

3,21 

3.82 

3.23 

3.80 

3. 

25 

3.79 

3.26 

5 

6 

4.60 

3.86 

4.58 

3.88 

4.56 

3. 

90 

4.55 

3.92 

6 

7 

5.36 

4.50 

5.34 

4.52 

5.32 

4. 

55 

5.30 

4. 57 

7 

8 

6.13 

5.14 

6.11 

5.17 

6.08 

5. 

20 j 

6.06 

5.22 

8 

9 

6.89 

5.79 

6.87 

5.82 

6.84 

5. 

84 

6.82 

5. 87 

9 

10 

7.66 

6.43 

7.63 

6.46 

7.60 

6. 

49 | 

7.58 1 

6.53 

10 

11 

8.43 

7.07 

8.40 

7.11 

8.36 

7. 

14 

8.33 

7.18 

11 

12 

9.19 

7.71 

9.16 

7.75 

9.12 

7. 

79 

9.09 

7.83 

12 

13 

9.96 

8.36 

9.92 

8.40 

9.89 

8. 

44 | 

9.85 

8.49 

.3 

14 

10.72 

9.00 

10.69 

9.05 

10.65 

9. 

09 

10.61 

9.14 

14 

15 

11.49 

9.64 

11.45 

9.69 

11.41 

9. 

74 ; 

11.36 

9.79 

15 

16 

12.26 

10.28 

12.21 

10.34 

12.17 

10. 

39 

12.12 

10.44 

16 

17 

13.02 

10.93 

12.97 

10.98 

12.93 

11. 

04 

12.88 

11.10 

17 

18 

13.79 

11.57 

13.74 

11.63 

13.69 

11. 

69 

13.64 

11.75 

18 

19 

14.55 

12.21 

14.50 

12.28 

14.45 

12. 

34 

14.39 

12.40 

19 

20 

15.32 

12.86 

15.26 ; 

12.92 

15.21 

12. 

99 I 

15.15 

13.06 

20 

21 

16.09 

13.50 

16.03 

13.57 

15.97 

13. 

64 

15.91 

13.71 

21 

22 

16.85 

14.14 

16.79 

14.21 

16.73 

14. 

29 ! 

16.67 

14.36 

22 

23 

17.62 

14.78 

17.55 

14.86 

17.49 

14. 

94 j 

17.42 

15.01 

23 

24 

18.39 

15.43 

18.32 

15.51 

18.25 

15. 

59 , 

18.18 

15.67 

24 

25 

19.15 

16.07 

19.08 

16.15 

19.01 

16. 

24 

18.94 

16.32 

25 

26 

19.92 

16.71 

19.84 

16.80 

19.77 

16. 

89 

19.70 

16.97 

26 

27 

20.68 

17.36 

20.61 

17.45 

20.53 

17. 

54 ! 

20.45 

17.62 

27 

28 

21.45 

18.00 

21.37 

18.09 

21.29 

18. 

18 , 

21.21 

18.28 

28 

29 

22.22 

18.64 

22.13 

18.74 

22.05 

18. 

83 

21.97 

18.93 

29 

30 

22.98 

19.28 

22.90 

19.38 

22.8.1 

19 

48 ! 

22.73 

! 19.58 

30 

31 

23.75 

19.93 

23.66 

20.03 

23.57 

20 

13 

23.48 

20.24 

31 

32 

24.51 

20.57 

24.42 

20.68 

24.33 

20 

78 ■ 

24.24 

i20.89 

32 

33 

25.28 

21.21 

25.19 

21.32 

25.09 

21 

.43 

25.00 

21.54 

33 

O A 
O'Jr 

26.05 

21.85 

25.95 

21.97 

25.85 

Of» 

A* r* 

.08 

25.76 

22.19 

34 

35 

26.81 

22.50 

26.71 

22.01 

26.61 

oo 

/*» A* 

.73 

26.51 

!22.85 

35 

30 

27.58 

23.14 

27.48 

23.26 

27.37 

23 

.38 

27.27 

23.50 

36 

37 

28.31 

23.78 

28.24 

23.91 

28,13 

24 

.03 

28.03 

24.15 

37 

38 

29.11 

24.43 

29.00 

24.55 

28.90 

1 24 

.68 

28.79 

24.80 

38 

39 

29.88 

25.07 

29.77 

25.20 

29.66 

25 

.33 

29.54 

i 25.46 

39 

40 

30.64 

25.71 

30.53 

25.84 

1 30.42 

| 25 

.98 

30.30 

| 26 . 11 

1 40 

41 

31.41 

26.35 

31.29 

26.49 

| 31.18 

! 26 

.03 

31.06 

i 26.76 

41 

42 

32.17 

27.00 

32.06 

27.14 

31.94 

27 

.28 

31.82 

27.42 

42 

43 

32.94 

' 27.64 

32.82 

27.78 

32.70 

1 27 

.93 

32.58 

2S.07 

43 

44 

33.71 

i 28.28 

33.58 

28.43 

33.46 

i 28 

.58 

l 33.33 

28.72 

44 

45 

34.47 

28.93 

34.35 

29.08 

1 34.22 

29 

.23 

j 34.09 

29.37 

45 

46 

35.24 

|29.57 

35.11 

29.72 

134.98 

| 29 

.87 

34.85 

30.03 

46 

47 

36.00 

| 30.21 

35.87 

30.37 

35.74 

30 

.52 

i 35.61 

30.68 

47 

48 

| 36.77 

30.85 

36.64 

31.01 

36.50 

31 

.17 

36.36 

!31.33 

48 

49 

!37.54 

1 31.50 

37.40 

31.66 

37.26 

31 

.82 

37.12 

31.99 

49 

50 

1 38.30 

L 

i 32.14 

38.16 

32.31 

38.02 

32 

.47 

37.88 

32.64 

50 

6 

c 

r/3 

i-4 

a 

Dep. 

1 Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

| Hep- 

| Lat. 

<B 

O 

cd 

w 

• rM 

c 

50 Deg. 

49f Deg. 

49 h 

Deg. 

49} Deg. 


































































































TRAVERSE TABLE 


83 


* 

tn 

r—► 

P 

3 

O 

40 Deg, 

40j Deg. 

40^ Deg. 

401 Deg. 

| Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lilt. 

Dep. 

51 

39.07 

32.78 

38.92 

32.95 

38.78 

33.12 

38.64 

33.29 

j 51 

52 

39.83 

33.42 

39.69 

33.60 

39.54 

33.77 

39.39 

33.94 

52 

53 

40.60 

'34.07 

40.45 

34.24 

40.30 

34.42 

40.15 

34.60 

53 

54 

41.37 

34.71 

41.21 

34.89 

41.03 

35.07 

40.91 

35.25 

l 54 

55 

42.13 

36.35 

41.98 

35.54 

41.82 

35.72 

41.67 

35,90 

; 55 

56 

42.90 

36.00 

42.74 

36.18 

42.58 

36.37 

42.42 

36.55 

66 

57 

43.66 

36.64 

43.50 

36.83 

43.34 

37.02 

i 43.18 

37.21 

57 

58 

44.43 

37.28 

44.27 

37.48 

44.10 

37.67 

43.94 

37.86 

58 

59 

45.20 

37.92 

45.03 

38.12 

44.86 

38.32 

44.70 

38.51 

59 

60 

45.96 

38.57 

45.79 

38.77 

45.62 

38.97 

45.45 

39.17 

60 

61 

46.73 

39.21 

46.56 

39.41 

46.38 

39.62 

46.21 

39.82 

61 

62 

47.49 

39.85 

47.32 

40.06 

47.15 

40.27 

46.97 

40.47 

62 

63 

48.26 

40.50 

48.08 

40.71 

47.91 

40.92 

47.73 

41.12 

63 

64 

49.03 

41,14 

48.85 

41.35 

48.67 

41.56 

48.48 

41.78 

64 

65 

49.79 

41.78 

49.61 

42.00 

49.43 

42.21 

49.24 

42.43 

65 

66 

50.56 

42.42 

50.37 

42.64 

50.19 

42.86 

50.00 

43.08 

66 

67 

51.32 

43.07 

51.14 

43.29 

50.95 

43.51 

50.76 

43.73 

67 

68 

52.09 

43.71 

51.90 

43.94 

51.71 

44.16 

! 51.51 

44.39 

68 

69 

52.86 

44.35 

52.66 

44.58 

52.47 

44.81 

52.27 

45.04 

69 

70 

53.62 

45.00 

53.43 

45.23 

53.23 

45.46 

1 53.03 

45.69 

70 

71 

54.39 

45.64 

54.19 

45.87 

53.99 

46.11 

53.79 

46.35 

71 

72 

55.16 

46.28 

54.95 

46.52 

54.75 

46.76 

54.54 

47.00 

72 

73 

55.92 

46.92 

55.72 

47.17 

55.51 

47.41 

55.30 

47.65 

73 

74 

56.69 

47.57 

56.48 

47.81 

56.27 

48.06 

56.06 

48.30 

74 

75 

57.45 

48.21 

57.24 

48.46 

57.03 

48.71 

56.82 

48.96 

75 

76 

58.22 

48.85 

58.01 

49.11 

57.79 

49.36 

57.57 

49.61 

76 

77 

58.99 

49.49 

58.77 

49.75 

58.55 

50.01 

58.33 

50.26 

77 

78 

59.75 

50.14 

59,53 

50.40 

59.31 

50.66 

59.09 

50.92 

78 

79 

60.52 

50.78 

60.30 

51.04 

60.07 

51.31 

59.85 

51.57 

79 

80 

61.28 

51.42 

61.06 

51.69 

60.83 

51.96 

60.61 

52.22 

80 

81 

62.05 

52.07 

61.82 

52.34 

61.59 

52.61 

61.36 

52.87 

81 

82 

62.82 

52.71 

62.59 

52.98 

62.35 

53.25 

62.12 

53.53 

82 

83 

63.58 

53.35 

63.35 

53.63 

63.11 

53.90 

62.88 

54.18 

83 

84 

64.35 

53.99 

64.11 

54.27 

63.87 

54.55 

63.64 

54.83 

84 

85 

65.11 

54.64 

64.87 

54.92 

64-63 

55.20 

64.39 

55.48 

85 

86 

65.88 

55.28 

65.64 

55.57 

65* 39 

55.85 

65.15 

56.14 

86 

87 

66.65 

55.92 

G6.40 

56.21 

66.16 

56.50 

65.91 

56.79 

87 

83 

67.41 

56.57 

67.16 

56.86 

66.92 

57.15 

66.67 

57.44 

88 

89 

68.18 

57.21 

67.93 

57.50 

67.68 

57.80 

67.42 

58.10 

89 

5 90 

68.94 

57.85 

68.69 

58.15 

68.44 

58.45 

68.18 

58.75 

90 

91 

69.71 

58.49 

69.45 

58.80 

69.20 

59.10 

68.94 

59.40 

91 

92 

70.48 

59.14 

70.22 

59.44 

69.96 

59.75 

69.70 

60.05 

92 

93 

71.24 

59.78 

70.98 

60.09 

70.72 

60.40 

70.45 

60.71 

93 

94 

72.01 

60.42 

71.74 

60.74 

71.48 

61.05 

71.21 

61.36 

94 

95 

72.77 

61.06 

72.51 

61.38 

72.24 

61.70 

71.97 

62.01 

95 

96 

73.54 

61.71 

73.27 

62.03 

73.00 

62.35 

72.73 

62.66 

96 

97 

74.31 

62.35 

74.03 

62.67 

73.76 

63.00 

73.48 

63.32 

97 

08 

75.07 

62.99 

74.80 

63.32 

74.52 

63.65 

74.24 

63.9? 

98 

99 

75.84 

63.64 

75.56 

63.97 

75.28 

64.30 

75.00 

64.62 

99 

100 

76.60 

64.28 

76.32 

64.61 

76.04 

64.94 

75.76 

65.28 

100 

6 

o 

fi 

Dep. 

Lat. 

Dep. 

Lat,. 

Dep. 

Lat. 

Dep. 

> 

Lat. 

1 

6 

o 

a 

ri 

• 

a 

50 Deg. 

49f Deg. 

49£ Deg. 

49| Deg. 

3 i 

































































































































84 


TRAVERSE TABLE 


Distance. 

41 Deg. 

4H Deg. 

4 U 

Deg. 

41| Deg. 

a 
*— • 

xji 

<r+ 

P 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

a 

p 

1 

0.75 

0.66 

0.75 

0.C6 

0.75 

0.66 

0.75 

0.67 

i 

O 

/V 

1.51 

1.31 

1.50 

1.32 

1.50 

1.33 

1.49 

1.33 

2 

3 

2.26 

1.97 1 

2.26 

1.98 

2.25 

1.99 

2.24 

2.00 

3 

4 

3.02 

2.62 

3.01 

,2.64 

3.00 

2.65 

2.98 

2.66 

4 

5 

3.77 

3.28 

3.76 

3.30 

3.74 

3.31 ; 

3.73 

3.33 

5 

6 

4.53 

3.94 j 

4.51 

3 . 90 

| 4.49 

3.98 

4.48 

4.00 

6 

7 

5.28 

4.59 1 

5.26 

4.62 

i 5.24 

4.64 

5.22 

4.66 

7 

8 

6.04 

5.25 

6.01 

5.27 

5 99 

5.30 

5.97 

5.33 

8 

9 

8.79 

5.90 

6.77 

5.93 

6.74 

5.96 

6.71 

5.99 

9 

10 

7.55 

6.56 

7.52 

6.59 

7.49 

6.63 

7.46 

6.66 

10 

11 

8 .30 

7.22 

8.27 

7.25 

8.24 

7.29 

8.21 

7.32 

11 

12 

9.06 

7.87 

9.02 

7.91 

8.99 

7.95 

8.95 

7.99 

12 

13 

9.81 

8.53 

9.77 

8.57 

9.74 

8.61 

9.70 

8.66 

13 

14 

10.57 

9.18 

10.53 

9.23 

10.49 

9.28 ' 

JO. 44 

9.32 

n 

15 

11.32 

9.84 

11.28 

9.89 

11.23 

9.94 

11.19 

9.99 

15 

16 

12.08 

10.50 

12.03 

10.55 

11.98 

10.60 

11 . 94 

10.65 

16 

17 

12.83 

11.15 

12.78 

11.21 

12.73 

1 1 .26 

12.68 

11.32 

17 

18 

13.58 

11.81 

13.53 

11.87 

13.48 

11 .93 

13.43 

11.99 

18 

19 

14.34 

12.47 1 

14.28 

12.53 

14.23 

12.59 

14.18 

12.65 

19 

20 

15.09 

13.12 j 

15.04 

13.19 

14.98 

13.25 

14.92 

13.32 

20 

21 

15.85 

13.78 I 

15.79 

13.85 

15.73 

13.91 

15.67 

13.98 

21 

22 

16.60 

14.43 I 

16.54 

14.51 

16.48 

14.58 

16.41 

14.65 

22 

23 

17.36 

15.09 

17.29 

15.16 

17.23 

15.24 

17.16 

15.32 

23 

24 

18.11 

15.75 ! 

18.04 

15.82 

17.97 

15.90 

17.91 

15.98 

24 

25 

18.87 

16.40 

18.80 

16.48 

18.72 

16.57 

18.65 

16.65 

25 

26 

19.62 

17.06 

19.55 

17.14 

19.47 

17.23 

19.40 

17.31 

26 

27 

20.38 

17.71 

20.30 

17.80 

20.22 

17.89 

20.14 

17.98 

27 

28 

21.13 

18.37 

21.05 

18.46 

20.97 

18.55 

20.89 

18.64 

28 

29 

21.89 

19.03 

21.80 

19.12 

21.72 

19.22 

21.64 

19.31 

29 

30 

22.64 

19.68 

22.56 

19.78 

22.47 

19.88 

22.3S 

19.98 

30 

31 

23.40 

20.34 

23.31 

20.44 

23.22 

20.54 

23.13 

20.64 

31 

32 

24.15 

20.99 

24.06 

21.10 

23.97 

21.20 

23.87 

21.31 

32 

33 

24.91 

21.65 

24.81 

21.76 

24.72 

21.87 

24.62 

21.97 

33 

34 

25.66 

22.31 

25.56 

22.42 

25.4j6 

22.53 

25.37 

22.64 

34 

35 

26.41 

22.96 

26.31 

23.08 

26.21 

23.19 

26.11 

23.31 

35 

36 

27.17 

23.62 

27.07 

23.74 

26.96 

23.85 

26.86 

23.97 

30 

37 

27.92 

24.27 

27.82 

24.40 

27.71 

24.52 

27.60 

24.64 

37 

38 

28.68 

24.93 

28.57 

25.06 

28.46 

25.18 

28.35 

25.30 

38 

39 

29.43 

25.59 

29.32 

25.71 

29.21 

25.84 

29.10 

25.97 

39 

40 

30.19 

26.24 

30.07 

26.37 

29.96 

26.50 

29.84 

26.64 

40 

41 

30.94 

26.90 

30.83 

27.03 

30.71 

27.17 

30.59 

27.30 

41 

42 

31.70 

27.55 

31.58 

27.69 

31.46 

27.83 

31.33 

27.97 

42 

43 

32.45 

28.21 

32.33 

28 . 35 

32.21 

28.49 

32.08 

28.63 

43 

44 

33.21 

28.87 

133.08 

29.01 

32 . 95 

29.16 

32.83 

29.30 

44 

45 

33.96 

29.52 

!33.83 

29.67 

33.70 

29.82 

33.57 

29.97 

45 

46 

34.72 

30.18 

34.58 

30.33 

34.45 

30.48 

34.32 

30.63 

46 

47 

35.47 

30.83 

!35 . 34 

30.99 

35.20 

31.14 

35.06 

31.30 

47 

48 

48 

36.23 

31.49 

136.09 

31.65 

35.95 

31.81 

35.81 

31 96 

49 

30 . 98 

32.15 

36.84 

32.31 

36.70 

32.47 

36.56 

32. 63 

(59 

50 

37.74 

32.80 

37.59 

32.97 

37.45 

33.13 

37.30 

|33.29 

50 

© 

o 

*-« 

Dep. 

Lat. 

Dep. 

Lat. 

| Dep. 

Lat. 

Dep. 

Lat. 

C 

cJ 

cn 

a 

49 Deg. 

j 48f Deg. 

481, Deg. 

481 Deg. 

cd 

+-> 

00 

£ 





























































































Distance.! OOOOOOOOOOOGOOOOOQO <><y>CT)CZ<J>C7>G'jttG^O* v’i|. onnTnc ,/, 

I w ^vj r- O’! W t- OCOGO-^C&Oi^OOtO*— O- <£> CO ^ C> O i ►£* CO h- OCOCCvioa>H^CJWH- ro CO <> rr> rn ^ CO tO *--] UJia P|U 


TRAVERSE TABLE 


83 


41 Deg. 

41$ Deg. 

41$ Deg. 

41$ Deg. 

O 

r/i 

r-* 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

Dep. 

3 

o 

CO 

38.49 

33.46 

38.34 

33.63 

38.20 

33.79 

38.05 

33.96 

~51 

39.24 

34.12 

39.10 

34.29 

38.95 

34.46 

38.79 

34.63 

52 

1 40.09 

34.77 

39.85 

34.95 

39.69 

35.12 

39.54 

35.29 

53 

40.75 

35.43 

40.60 

35.60 

40.44 

35.78 

40.29 

35.96 

54 

41.51 

36.08 

41.35 

36.26 

41.19 

36.44 

41.03 

36.62 

55 

42 26 

36.74 

42.10 

36.92 

41.94 

37.11 

41.78 

37.29 

56 

43 02 

37.40 

42.85 

37.58 

42.69 

37.77 

42.53 

37.96 

57 

43.77 

38.05 

43.61 

38.24 

43.44 

38.43 

43.27 

38.62 

58 

44.53 

38.71 

44.36 

38.90 

44.19 

39.09 

44.02 

39.29 

59 

45.28 

39.36 

45.11 

39.56 

44.94 

39.76 

44.76 

39.95 

60 

46.04 

40.02 

45.86 

40.22 

45.69 

40.42 

45.51 

40.62 

61 

46.79 

40.68 

46.61 

40.88 

46.44 

41.08 

46.26 

41.28 

62 

47.55 

41.33 

47.37 

41.54 

47.18 

41.75 

47.00 

41.95 

63 

48.30 

41.99 

48.12 

42.20 

47.93 

42.41 

47.75 

42.62 

64 

49.06 

42.64 

48.87 

42.86 

48.68 

43.07 

48.49 

43.28 

65 

49.81 

43.30 

49.62 

43.52 

49.43 

43.73 

49.24 

43.95 

66 

50.57 

43.98 

50.37 

44.18 

50.18 

44.40 

49.99 

44.61 

67 

51.32 

44.61 

51.13 

44.84 

50.93 

45.06 

50.73 

45.28 

68 

|52.07 

45.27 

51.88 

45.49 

51.68 

45.72 

51.48 

45.95 

69 

52.83 

45.92 

52.63 

46.15 

52.43 

46.38 

52.22 

46.61 

70 

53.58 

46.58 

53.38 

46.81 

53.18 

47.05 

52.97 

47.28 

71 

54.34 

47.24 

54.13 

47.47 

53.92 

47.71 

53.72 

47.94 

72 

55.09 

47.89 

54.88 

43.13 

54.67 

48.37 

54.46 

48.61 

73 

55.85 

48.55 

55.64 

48.79 

55.42 

49.03 

55.21 

49.28 

74 

56.60 

49.20 

56.39 

49.45 

56.17 

49.70 

55.95 

49.94 

75 

57.36 

49.86 

57.14 

50.11 

56.92 

50.36 

56.70 

50.61 

76 

58.11 

50.52 

57.89 

50.77 

57.67 

51.02 

57.45 

51.27 

77 

58.87 

51.17 

58.64 

51.43 

58.42 

51.68 

58.19 

51.94 

78 

59.62 

51.83 

59.40 

52.09 

59.17 

52.35 

58.94 

52.60 

79 

60.38 

52.48 

60.15 

52.75 

59.92 

53.01 

59.6S 

53.27 

80 

61.13 

53.14 

60.90 

53.41 

60.67 

53.67 

60.43 

53.94 

81 

61.89 

53.80 

61.65 

54.07 

61.4) 

54.33 

61.18 

54.60 

82 

62.64 

54.45 

62.40 

54.73 

62.16 

55.00 

61.92 

55.27 

83 

63.40 

55.11 

63.15 

55.38 

62.91 

55.66 

62.67 

55.93 

84 

64.15 

55.76 

63.91 

56.04 

63.66 

56.32 

63.41 

56.60 

85 

64.90 

56.42 

64.66 

56.70 

64.41 

56.99 

64.16 

57.27 

86 

|65.66 

57.08 

65.41 

57.36 

65.16 

57.65 

64.91 

57.93 

87 

1 66.41 

57.73 

66.16 

58.02 

65.91 

58.31 

i65.65 

58.60 

88 

67.17 

58.39 

66.91 

58.68 

66.66 

58.97 

66.40 

59.26 

89 

67.92 

59.05 

67.67 

59.34 

67.41 

59.64 

i67.15 

59.93 

90 

68.68 

59.70 

68.42 

60.00 

68.15 

60.30 

67.89 

60.60 

91 

69.43 

60.36 

69.17 

60.68 

68.90 

60.96 

68.64 

61.26 

92 

70.19 

61.01 

69.92 

61.32 

69.65 

61.62 

69.38 

61.93 

93 

70.94 

61.67 

70.67 

61.98 

70.40 

62.29 

70.13 

62.59 

94 

: 71.70 

62.33 

71.43 

62.64 

71.15 

62.95 

70.88 

63.26 

95 

72.45 

62.98 

72. 18 

63.30 

71.90 

63.61 

71.62 

63.92 

96 

73.21 

63.64 

72.93 

63.96 

72.65 

64.27 

72.37 

64.59 

97 

73.96 

64,29 

173.68 

64.62 

73.40 

61.94 

73.11 

65.26 

98 

74.72 

64.95 

74.43 

65.28 

74.15 

65.60 

73.86 

65.92 

99 

75.47 

65.61 

75.18 

65.93 

74.90 

66.26 

74.61 

66.59 

100 

Def 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

<r 

o 

2 

49 Deg. 

48J Deg. 

48$ Deg. 

48$ Deg. 

cd 

ao 

p 










































































































86 


traverse taele. 


Distance. 

42 Deg. 

42k 

42^ Deg. 

42 1 Deg 

Distance. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. ; 

~ l" 

0.74 

0.67 

0.74 

0.67 

0.74 

0.68 

0.73 

0.68 ! 

1 

2j 

1.49 

1.34 

1.48 

1.34 

1.47 

1.35 

1.47 

1.36 

2 

3 ! 

2.23 

2.01 

2.22 

2.02 

2.21 

2.03 

2.20 

2.01 

3 

'1 

4 

2.97 

2.68 

2.96 

2.69 

2.95 

2.70 

2.94 

2.72 

5 

3.72 

3.35 

3.70 

3.36 

3.69 

3.38 

3.67 

3.39 

5 

6 

4.46 

4.01 

4.44 

4.03 

4.42 

4.05 

4.41 

4.07 

fi 

7 

5.20 

4.68 

5.18 

4.71 

5.16 

4.73 1 

5.14 ! 

4.75 

7 

8 

5.96 

5.35 

5.92 | 

5.38 

5.90 

5.40 1 

5.87 | 

5.43 

S 

9 

6.69 

6.02 

6.66 

6.05 

6.64 

6.08 

6.61 ; 

6.11 

9 

10 

7.43 

6.69 

7.40 | 

6.72 

7.37 

6.76 ! 

7.34 | 

6.79 

10 

11 

8.17 

7.36 

8.14 

7.40 

8.11 

7.43 

8.08 : 

7.47 

11 

12 

8.92 

8.03 

8.88 1 

8.07 

8.85 

8.11 | 

8.81 

8. 15 

12 

13 

9.66 ! 

8.70 

9.62 1 

8.74 

9.58 

8.78 | 

9.55 ; 

8.82 

13 

14 

10.40 ! 

9.37 

10.36 

9.41 

10.32 

9.46 | 

10.28 

9.50 

14 

16 

11.15 

10.04 

11.10 

10.09 

11.06 

10.13 

11.01 

to. IS 

15 

16 

11.89 

10.71 

11.84 

10.76 

11.80 

10.81 

11.75 

10.86 

16 

17 

12.63 

11.38 

12.58 

11.43 

12.53 

11.48 

12.48 

11.54 

17 

18 

13.38 

12.04 

13.32 

12.10 

13.27 

12.16 

13.22 

12.22 

18 

19 

14.12 

12.71 

14.06 

12.77 

14.01 

12.84 

13.95 

12.90 

19 

20 

14.86 

13.38 

14.80 

13.45 

14.75 

13.51 

14.69 

13.58 

20 

21 

15.61 

14.05 

1 5.54 

14.12 

15.48 

14.19 

15.42 

14.25 

21 

22 

16.35 

14.72 

16.28 

14.79 

16.22 

14.86 

16.16 

14,93 

22 

23 

17.09 

15.39 1 

17.02 

15.46 

16.96 

15.54 

16.89 

15.61 

23 

24 

17.84 

16.06j 

17.77 

16.14 

17.69 

16.21 

17.62 

16.29 

24 

26 

18.58 

16.73 

18.51 

16.81 

18.43 

16.89 

18.36 

16.97 

25 

26 

19.32 

17.40 

19.25 

17.48 

19.17 

17.57 

19.09 

17.65 

26 

27 

20.06 

18.07 

19.99 

18.15 

19.91 

18.24 

19.83 

18.33 

27 

2S 

20.81 

18.74 

20.73 

18.83 

20.64 

18.92 

20.56 

19.01 

28 

29 

21.55 

19.40 

21.47 

19.50 

21.38 

19.59 i 

21.30 

19.69 

29 

30 

oo f>q 

20.07 

22.21 

20.17 

22.12 

20.27 

22.03 

20.36 

30 

31 

23.04 

20.74 

22.95 

20.84 

22.86 

20.94 

22.76 

21.04 

31 

32 

23.78 

21.41 

23.69 

21.52 

123.59 

21.62 

23.50 

21.72 

32 

33 

24.52 

22.08 

24.43 

22.19 

24.33 

22.29 

.24.23 

. 22. •&. 

. -3;i 

34 

25.27 

22.75 

25. 17 

22.86 

25.07 

22.97 

24.97 

j23.08 

34 

36 

26.01 

23.42 

25.91 

23.53 

25.80 

23.65 

1 25.70 

l 23.76 

35 

36 

| 26 . 75 

24.09 

26.65 

24.21 

26.54 

24.32 

! 26.44 

24.44 

36 

37 

[ 27 50 

1 24.76 

27.39 

24.83 

27.28 

; 25 . 00 

27. 17 

i 25.12 

37 

38 

28.24 

25.43 

28.13 

25 . 55 

28 . 02 

25.67 

I 27.90 

25 . 79 

38 

39 

! 28.98 

126.10 

28.87 

26.22 

28.75 

26.35 

28.64 

126.47 

39 

40 

29.73 

1 26.77 

29.61 

26.89 

29.49 

27.02 

! 29.37 

! 27.15 

40 

41 

30.47 

27.43 

30.35 

27.57 

30.23 

27.70 

,30.11 

j 27.83 

41 

42 

31.21 

28.10 

31.09 

oo 94 

30.97 

28.37 

30.84 

! 28.5i 

42 

43 

31.96 

28.77 

31.83 

28.91 

31.70 

29.05 

|31.58 

1 29.19 

43 

44 

32.70 

29.44 

|32.57 

29.58 

32.44 

29.73 

32.31 

29.87 

44 

46 

33.44 

! 30.11 

33.31 

[30.26 

33.18 

30.40 

33.04 

30.55 

15 

46 

34.18 

30.78 

34.05 

30.93 

33.91 

31.08 

33.78 

9 1 99 

46 

47 

34.93 

31.45 

34.79 

31.60 

34.65 

31.75 

134.51 

31.90 

47 

48 

35.67 

1 32.12 

35.53 

32.27 

35.39 

32.43 

135.25 

' 32.58 

48 

49 

36.41 

32.79 

36.27 

32.95 

36.13 

33.10 

35.98 

133.26 

49 

60 

!37.16 

33.46 

37.01 

33.62 

36.86 

33.78 

36.72 

|33.94 

50 

a> 

O 

a 

sJ 

*—* 

! Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat 

Distance. 

43 Deg. 
i 

47f Deg. 

41 i Deg. 

4li Deg. 





































































































TRAVERSE TABLE- 


87 


►—< 
W 
)— » 
r JB 

p 

i 

42 Deg. 

42:; Deg. 

42i Deg 

• 

42f Deg 

• 

>-« 

►— • 
m 

e-« 

p5 

o 

? 

Lat# 

Dep. 

Lat. 

Dep. 

Lat. 

De 

r* 

Lat. 

Dep. 

s 

o 

» 

• 

51 

37 

.90 

34. 

13 

37 

.75 

34. 

29 

37 

60 

34. 

46 

37. 

45 

34. 

62 

51. 

52 

38 

.64 

34. 

79 

38 

.49 

34. 

96 

3S 

34 

35. 

13 

38. 

18 

35. 

30 j 

52 

53 

39 

.39 

35. 

46 

39 

.23 

35. 

64 

39 

08 

35. 

81 

38. 

92 

35. 

98 

53 

54 

40 

. 13 

36. 

13 

39 

.97 

36. 

31 

39 

.81 

36. 

48 

39 

65 

36. 

68 | 

51 

55 

40 

.87 

38. 

80 

40 

.71 

36. 

98 

40 

55 

37. 

16 

40 

39 

37. 

33 

55 

56 

41 

.62 

37. 

47 

41 

.45 

37. 

65 

41 

.29 

37. 

83 

41 

12 

38. 

01 

56 

57 

42 

.36 

33. 

14 

42 

.19 

38. 

32 

42 

.02 

38. 

51 

41 

86 

38. 

69 

57 

58 

43 

.10 

33. 

81 

42 

.93 

39. 

00 

42 

.76 

39. 

IS 

42 

59 

39. 

37 

58 

59 

43 

.85 

39. 

48 

43 

.67 

39. 

67 

43 

.50 

39. 

86 

43 

32 

40 

05 

59 

GO 

44 

.59 

40. 

15 

44 

.41 

40. 

34 

1 44 

.24 

40. 

54 | 

44 

06 

40 

73 

60 

61 

45 

.33 

40. 

82 

45 

. 15 

41. 

01 

44 

.97 

41. 

21 

44 

.79 

41 

41 

61 

62 

46 

.07 

41. 

49 

45 

.89 

41. 

69 

45 

.71 

4i . 

39 I 

45 

.53 

42 

09 

62 

63 

46 

.82 

42. 

16 

46 

.63 

42. 

36 

46 

.45 

42. 

56 

46 

.26 

42 

76 

63 

64 

47 

.56 

42. 

82 

47 

.37 

43. 

03 

47 

.19 

43. 

24! 

47 

.00 

43 

44 

64 

65 

48 

.30 

43. 

49 

48 

.11 

43. 

70 

47 

.92 

43. 

91 

47 

.73 

44 

12 

65 

66 

49 

.05 

44. 

16 

48 

.85 

44. 

38 

48 

. 66 

44. 

59 j 

48 

.47 

44 

.80 

66 

67 

49 

.79 

44. 

83 

49 

.59 

45. 

05 

49 

.40 

45. 

26 

49 

.20 

45 

.48 

67 

68 

50 

.53 

45 

50 

50 

.33 

45. 

72 

50 

.13 

45. 

94 

49 

.93 

46 

.16 

68 

69 

51 

.28 

46. 

17 

51 

.07 

46. 

39 

50 

.87 

46. 

62 

50 

.67 

46 

.84 

69 

70 

52 

.02 

46. 

84 

51 

.82 

47. 

07 

51 

.61 

47. 

29 

51 

.40 

47 

.52 

70 

71 

52 

.76 

47. 

51 

52 

.56 

47. 

74 

52 

.35 

47. 

97 

52 

.14 

4S 

.19 

71 

72 

53 

.51 

48. 

18 

53 

.30 

48. 

41 

53 

.08 

48. 

64 

52 

.87 

43 

.87 

72 

73 

54 

.25 

48. 

85 

54 

.04 

49. 

08 

53 

.82 

49. 

32 

53 

.61 

49 

.55 

73 

74 

54 

.99 

49. 

52 

54 

.78 

49. 

76 

54 

.56 

49. 

99 

54 

.34 

50 

.23 

74 

75 

55 

.74 

50. 

18 

55 

.52 

50. 

43 

55 

.30 

50. 

67 

55 

.07 

50 

.91 

75 

76 

56 

.48 

50. 

85 

56 

.26 

51. 

10 

56 

.03 

51. 

34 

I 55 

.81 

51 

.59 

76 

77 

57 

.22 

51. 

52 

57 

.00 

51. 

77 

56 

.77 

52. 

02 

! 56 

. 54 

52 

.27 

77 

78 

57 

.97 

52. 

19 

57 

.74 

52. 

44 

57 

.51 

52. 

70 

! 57 

.28 

52 

.95 

78 

79 

58 

.71 

52. 

88 

58 

.43 

53. 

12 

58 

.24 

53. 

37 

! 58 

.01 

53 

.63 

79 

80 

59 

.45 

53. 

53 

59 

.22 

53. 

79 

58 

.98 

54. 

05 

58 

.75 

54 

.30 

80 

81 

60 

.19 

54. 

20 

59 

.96 

54. 

46 

59 

.72 

54. 

72 

59 

.48 

54 

.98 

81 

82 

60 

.94 

54. 

87 

60 

.70 

55. 

13 

60 

.46 

55. 

40 

60 

.21 

55 

.66 

82 

83 

61 

.63 

55. 

54 

61 

.44 

55. 

81 

61 

.19 

56. 

07 

! 60 

.95 

56 

.34 

83 

84 

62 

.42 

58. 

21 

62 

. 18 

56. 

48 

61 

.93 

56. 

75 

1 61 

.68 

57 

.02 

84 

85 

63 

. 17 

56. 

S3 

62 

.92 

57. 

15 

62 

.67 

57. 

43 

1 62 

.42 

57 

.70 

85 

86 

63 

.91 

57. 

55 

63 

.66 

57. 

82 

63 

.41 

58. 

10 

63 

. 15 

58 

.33 

86 

87 

64 

. 65 

58. 

21 

64 

.40 

58. 

50 

64 

.14 

58. 

78 

63 

.89 

59 

.06 

87 

88 

65 

.40 

53. 

88 

65 

. 14 

59. 

17 

64 

.88 

59. 

45 

64 

.62 

59 

.73 

88 

89 

66 

.14 

59. 

55 

65 

.88 

59. 

84 

65 

.62 

60. 

13 

65 

.35 

60 

.41 

89 

90 

66 

.83 

60. 

22 

66 

.62 

60. 

51 

66 

.35 

60. 

80 

66 

.09 

61 

.09 

90 

91 

67 

.63 

60. 

89 

67 

.38 

61. 

19 

67 

.09 

61. 

48 

i 66 

.82 

61 

.77 

91 

92 

63 

.37 

61. 

56 

6S 

.10 

61. 

SS 

67 

.83 

62. 

15 

67 

.56 

62 

.45 

92 

93 

69 

.11 

62. 

23 

68 

.84 

62. 

53 

68 

.57 

62. 

83 

! 68 

.29 

63 

.13 

93 

94 

69 

.86 

62. 

90 

69 

.58 

63. 

20 

69 

.30 

63. 

51 

! 09 

.03 

63 

.81 

94 

95 

70 

.60 

63. 

57 

70 

.32 

63. 

87 

70 

.04 

64. 

18 

: 69 

.76 

64 

.49 

95 

96 

71 

.34 

64. 

24 

71 

.06 

64. 

55 

70 

.78 

64. 

86 

70 

.49 

65 

. 16 

96 

97 

72 

.03 

64. 

91 

71 

.80 

65. 

22 

71 

.52 

65. 

53 

71 

.23 

65 

.84 

97 

93 

72 

.83 

65. 

57 

72 

.54 

05. 

89 

72 

. 25 

66. 

21 

1 71 

. 96 

66 

.52 

98 

99 

73 

.57 

66. 

24 

73 

.28 

66. 

56 

72 

. 99 

68. 

88 

1 72 

.70 

67 

.20 

99 

100 

74 

.31 

66. 

91 

74 

.02 

67. 

24 

73 

.73 

67. 

56 

7.3 

.43 

67 

.88 

100 

6 

O 

H 

D 

ep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat, 

6 

u 

G 

yj 

C 

48 Deg. 

47f Deg 


All Deg. 


il\ Deg 


■4~> 

co 

.1 





















































































































88 


TRAVERSE TABLE. 


Distance. 

43 Deg. 

43$ Deg< 

43 ^ Deg. 

43f Deg. 

C 

p 

Lat. 1 

Dep. 

i 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

3 

n 

s 

1 

0.73 

0.68 

0.73 

0.69 

0.73 

0.69 

0.72 

0.69 

1 

2 

1.40 

1 .36 I 

1.46 

1.37 

1.45 

1.38 

1.44 

1.38 

2 

3 

2.19 

2.05 

2.19 

2.06 

2.18 

2.07 

2.17 

2.07 

3 

4 

2.93 

2.73 

2.91 

2.74 

2.90 

2.75 

2.89 

2 77 

4 

5 

3.66 

3.41 

3.64 

3.43 

3.63 

3.44 

3.61 

3.46 

3 

6 

4.39 

4.09 

4.37 

4.11 

4.35 

4.13 

4.33 

4.15 

6 

7 

5.12 

4.77 

5.10 

4.80 

5.08 

4.82 

5.06 

4.84 

7 

8 

5.85 

5.46 

5.83 

5.48 

5. SO 

5.51 

5.78 

5.53 

8 

9 

6.58 

6.14 

6.56 

6.17 

6.53 

6.20 

6.50 

6.22 

9 

10 

7.31 

6.82 

7.28 

6.85 

7.25 

6.88 

7.22 

6 92 

10 

11 

8.04 

7.50 

8.01 

7.54 

7.98 

7.57 

7.95 

7.61 

11 

12 

8.78 

8.18 

8.74 

8.22 

8.70 

8.26 

8.67 

8.30 

12 

13 

9.51 

8.87 

9.47 

8.91 

9.43 

8.95 

9.39 

8.99 

13 

14 

10.24 

9.55 

10.20 

9.59 

10.16 

9.64 

10.11 

9.68 

14 

15 

10.97 

10.23 

10.93 

10.28 

10.88 

10.33 

10.84 

10.37 

15 

16 

11.70 

10.91 

11.65 

10.96 

11.61 

11.01 

11.56 

11.06 

16 

17 

12.43 

11.59 

12.38 

11.65 

12.33 

11.70 

12.28 

11.76 

17 

18 

13. 16 

12.28 

13.11 

12.33 

13.06 

12.39 

13.00 

12.45 

18 

19 

13.90 

12.96 

13.84 

13.02 

13.78 

13.08 

13.72 

13.14 

19 

20 

14.63 

13.64 

14.57 

13.70 

14.51 

J 3.77 

14.45 

13.83 

20 

21 

15.36 

14.32 

15.30 

14.39 

15.23 

14.46 

15.17 

14.52 

21 

22 

16.09 

15.00 

18.02 

15.07 

15.96 

15.14 

15.89 

15.21 

22 

23 

16.82 

15.69 

16.75 

15.76 

1G.68 

15.83 

16.61 

15.90 

23 

24 

17.55 

16.37 

17.48 

16.44 

17.41 

16.52 

17.34 

16.60 

24 

25 

18.28 

17.05 

18.21 

17.13 

18.13 

17.21 

18.06 

17.29 

25 

26 

19.02 

17.73 

18.94 

17.81 

18.86 

17.90 

18.78 

17.98 

26 

27 

19.75 

18.41 

19.67 

18 50 

19.53 

18.59 

19.50 

18.67 

27 

28 

20.48 

19.10 

20.39 

19.19 

20.3L 

19.27 

20.23 

19.36 

28 

29 

21.21 

19.78 

21.12 

19.87 

21.04 

19.96 

20.95 

20.05 

29 

30 

21.94 

20.46 

21.85 

20.56 

21.76 

20.65 

21.67 

20.75 

30 

31 

22.67 

21.14 

22.58 

21.24 

22.49 

21.34 

22.39 

21.44 

Ol 
tj l 

32 

23.40 

21.82 

23.31 

21.93 

23.21 

23.03 

23.12 

22.13 

32 

33 

24.13 

22.51 

24.04 

22.61 

23.94 

22.72 

23.84 

22.82 

33 

34 

24.87 

23.19 

24.7C 

23.30 

24.66 

23.40 

24.56 

23.51 

34 

35 

25.60 

23.87 

25.49 

23.98 

25.39 

24.09 

25.28 

24.20 

35 

36 

26.33 

24.55 

26.22 

24.67 

26.11 

24.70 

26.01 

24.89 

36 

37 

27.06 

25.23 

26.95 

25.35 

26.84 

25.47 

26.73 

25.59 

37 

38 

27.79 

25.92 

27.68 

26.04 

27.56 

26.16 

27.45 

26.28 

OQ 

oo 

39 

28.52 

26.60 

28.41 

26.72 

28.29 

26.85 

28.17 

26.97 

39 

40 

29.25 

27.28 

29.13 

27.41 

29.01 

27.53 

28.89 

27.66 

40 

41 

29.99 

27.96 

29.86 

28.09 

29.74 

28.22 

29.62 

28.35 

41 

42 

30.72 

28.64 

30.59 

28.78 

30.47 

28.91 

30.34 

29.04 

42 

43 

31.45 

29.33 

31.32 

29.46 

31.19 

29.60 

31.06 

29.74 

43 

44 

32.18 

30.01 

32.05 

30.15 

31.92 

30.29 

31.78 

30.43 

44 

45 

32.91 

30.69 

32.78 

30.83 

32.64 

30.98 

32.51 

31.12 

1 45 

46 

33.64 

31.37 

33.5 i 

31.52 

33.37 

31.68 

33.23 

31.81 

j 46 

47 

31.37 

32.05 

34.23 

32.20 

34.09 

32.35 

33.93 

32.50 

47 

48 

35.10 

32.74 

34.96 

32.89 

34.82 

33.04 

3A.G7 

! 33.19 

48 

49 

35.84 

33.42 

35.69 

33.57 

35.54 

33.73 

35.40 1 33 88 

49 

50 

36.57 

34.10 

36.42 

34.26 

36.27 

34.42 

3u. 12 <| bv.oS 

50 

O 

V 

£ 

Dep. 

Lat. 

Dep. 


Dep. 

Lat. 

Dsp. 

L*-' 

CJ 

o 

c 

cJ 

73 
•»—« 

Q 

47 Deg. 

46| Deg. 

46$ Deg. 

46$ Deg 

ri 

02 

J 


























































































































TRAVERSE TABLE. 


89 


o 

w* 

P 

43 Deg. 

43} Deg. 

431 

Deg. 

43} Deg. 

Distance. 

S3 

a 

a 

• 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

51 

37.30 

34.78 

37.15 

34.94 

36.99 

35711 

36.84 

35.27 

51 

52 

38.03 

35.46 

37.88 

35.63 

37.72 

35.79 

37.56 

35.96 

52 

53 

38.76 

36.15 

38.60 

36.31 

38.44 

36.48 

38.29 

36.65 

53 

64 

39.49 

36.83 

39.33 

37.00 

39.17 

37.17 

39.01 

37.34 

54 

55 

40.22 

37.51 

40.06 

37.69 

39.90 

37.86 

39.73 

38.03 

55 

56 

40.96 

38.19 

40.79 

38.37 

40.62 

38.55 

40.45 

38.72 

56 

57 

41.69 

38.87 

41.52 

39.06 

41.35 

39.24 

41.17 

39.42 

57 

58 

42.42 

39.56 

42.25 

39.74 

42.07 

39.92 

41.90 

40.11 

58 

59 

43.15 

40.24 

42.97 

40.43 

42.80 

40.61 

42.62 

40.80 

59 

60 

43.88 

40.92 

43.70 

41.11 

43.52 

41.30 

43.34 

41.49 

60 

61 

44.61 

41.60 

44.43 

41.80 

44.25 

41.99 

44.06 

42.18 

61 

62 

45.34 

42.28 

45. J 6 

42.48 

44.97 

42.68 

44.79 

42.87 

62 

63 

46.08 

42.97 

45.89 

43.17 

45.70 

43.37 

45.51 

43.57 

63 

64 

46.81 

43.65 

40.62 

43.85 

46.42 

44.05 

46.23 

44.20 

64 

65 

47.54 

44.33 

47.34 

44.54 

47.15 

44.74 

46.95 

44.95 

65 

66 

48.27 

45.01 

43.07 

45.22 

47.87 

45.43 

47.68 

45.64 

66 

67 

49.00 

45.69 

48.80 

45.91 

48.60 

46.12 

48.40 

46.33 

67 

68 

49.73 

46.38 

49.53 

46.59 

49.33 

46.81 

49.12 

47.02 

68 

69 

50.46 

47.06 

50.26 

47.28 

50.05 

47.50 

49.84 

47.71 

69 

70 

51.19 

47.74 

50.99 

47.96 

50.78 

48.18 

50.57 

48.41 

70 

71 

51.93 

48.42 

51.71 

4S.65 

51.50 

48.87 

51.29 

49.10 

71 

72 

52.66 

49.10 

52.44 

49.33 

52.23 

49.56 

52.01 

49.79 

72 

73 

53.39 

49.79 

53.17 

50.02 

52.95 

50.25 

52.73 

50.48 

73 

74 

54.12 

50.47 

53.90 

50.70 | 

53.68 

50.94 

53.45 

51.17 

74 

75 

54.85 

51.15 

54.63 

51.39 

54.40 

51.63 

54.18 

51.86 

75 

76 

55.58 

51.83 

55.36 

52.07 

55.13 

52.31 

54.90 

52.55 

76 

77 

56.31 

52.51 

56.08 

52.76 

55.85 

53.00 

55.62 

53.25 

77 

78 

57.05 

53.20 

56.81 

53.44 

56.58 

53.69 

56.34 

53.94 

78 

79 

57.78 

53.88 

57.54 

54.13 

57.30 

54.38 

57.07 

54.63 

79 

80 

58.51 

54.56 

58.27 

54.81 

58.03 

55.07 

57.79 

55.32 

80 

81 

59.24 

55.24 

59.00 

55.50 

58.70 

55.76 

58.51 

56.01 

81 

82 

59.97 

55.92 

59.73 

50.18 

59.48 

56.45 

59.23 

56.70 

82 

83 

60.70 

56.61 

60.45 

56.87 

60.21 

57.13 

I59.96 

57.40 

S3 

84 

61.43 

57.29 

61.18 

57.56 

60.93 

57.82 

I 60.68 

58.09 

84 

85 

62.17 

57.97 

61.91 

58.24 

61.60 

58.51 

61.40 

58.78 

85 

88 

62.90 

58.65 

62.64 

58.93 

62.38 

59.20 

62.12 

59.47 

88 

87 

63.63 

59.33 

63.37 

59.61 

63. H 

59.89 

62.85 

60.16 

87 

88 

64.36 

60.02 

64.10 

60.30 

63.83 

60.58 

63.57 

60.85 

88 

89 

65.09 

60.70 

64.82 

60.98 

64.56 

61.26 

64.29 

61.54 

89 

90 

65.82 

61.38 

65.55 

61.67 

65.28 

61.95 

65.01 

62.24 

90 

91 

66.55 

62.06 

66.28 

62.35 

66.01 

62.64 

65.74 

62.93 

91 

92 

67.2S 

62.74 

67.01 

63.04 

66.73 

63.33 

66.46 

63.62 

92 

93 

68.02 

63.43 

67.74 

63.72 

67.16 

64.02 

67.18 

64.31 

93 

94 

68.75 

64.11 

68.47 

64.41 

68.19 

64.71 

67.90 

65.00 

91 

95 

69.48 

64.79 

69.20 

65.09 

68.91 

65.39 

68.62 

65.69 

95 

96 

70.21 

65.47 

69.92 

65.78 

69.64 

68.08 

69.35 

66.39 

96 

97 

70.94 

66.15 

70.65 

68.46 

70.36 

66.77 

70.07 

67.08 

97 

98 

71.67 

66.84 

71.37 

67.15 

71.09 

67.46 

70.79 

67.77 

98 

99 

72.40 

67.52 

72.11 

67.83 

71.81 

68.15 

71.51 

68.46 

99 

100 

73.14 

68.20 

72.84 

68.52 

72.54 

08.84 

72.24 

69.15 

100 

o’ 

o 

r* 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

Dep. 

Lat. 

6 

o 

c 

cd 

c/: 

3 

47 Deg. 

461 Deg. 

i 

464 - 

Deg. 

46} Deg. 

so 

5 






































































































90 


TRAVERSE TABLE. 


00 ' 

c-* 

P 

44 Deg. 

44} Deg. 

►— 

O 

Q 

Lat. 

Dep. 

Lat. 

Dep. 

1 

0.72 

0.69 

0.72 

0.70 

O 

*4 

1.44 

1.39 

1.43 

1.40 

3 

2.16 

2.08 

2.15 

2.09 

4 

2.88 

2.78 

2.87 

2.79 

ir 

3.60 

3.47 

3.58 

3.49 

6 

4.32 

4.17 

4.30 

4.19 

7 

5.04 

4.86 

5.01 

4.88 

8 

5.75 

5.56 

5.73 

5.58 

9 

6.47 

6.25 

6.45 

6.28 

10 

7.19 

6.95 

7.16 

6.98 

11 

7.91 

7.64 

7.88 

7.68 

12 

8.63 

8.34 

8.60 

8.37 

13 

9.35 

9.03 

9.31 

9.07 

14 

10.07 

9.73 

10.03 

9.77 

15 

10.79 

10.42 

10.74 

10.47 

16 

11.51 

11.11 

11.46 

11.16 

17 

12.23 

11.81 

12.18 

11.86 

18 

12.95 

12.50 

12.89 

12.56 

19 

13.67 

13.20 

13.61 

13.26 

20 

14.39 

13.89 

14.33 

13.96 

21 

15.11 

14.59 

15.04 

14.65 

22115.83 

15.28 

15.76 

15.35 

2346.54 

15.98 

16.47 16.05 

2447.26 

16.67 

17.19 

16.75 

2547.98 

17.37 

17.91 

17.44 

2648.70 

18.06 

18.62 

18.14 

\ 27 

19.42 

18.76 

19.34 

18.84 

28 20.14 

19.45 

20.06 

19.54 

29 

20.86 

20.15 

20.77 

20.24 

30 

21.58 

20.84 

21.49 

20.93 

3i 

22.30 

21.53) 

22.21 

21.631 

32 23.02 

22.23 

22.92 

22.33; 

33 

23.74 

22.92 

23.64 

23.03 

34 

24.46 

23.62 

124.35 

23.72 

35)25.18 

24.31 

>25.07 

24.42 

36 25.90 

25.01 

'25.79 

25.12 

37 

26.62 

25.70 

26.50 

25.82 

38 27.33 

26.40 

27.22 

26.52 

39128.05 27.09 

27.94 

27.21 

40 

28.77 27.79 

28.65 

27.91 

41 

29749 28.48 

29.37)28.61 

42|20.21 

29. IS 

30.08 29.31 

43;30.93 

29.87 

30.80 30.00 

44 31.65 

30.56 

31.52 30.70 

45132.37 

31.26 

32.23 

31.40 

46 33.09 

31.95 

32.95 

32.10 

47 33.81 

32.65 

33.67 

32.80 

48 34.53 

33.34 

34.38 

33.49 

49)35.25 

34.04 

35.10 

34.19 

50 35.97 

34.73 

35.82 

34.89 

• 

0 

0 

CS 

j Dep. 

Lat. 

Dep. 

Lat. 

cd 

r X 

1 46 Deg 

451 Deg. 



16.40 

17.12 

17.83 

18.54 

19.26 

19.97 

20.68 


.92 19 
.631119 
.33;20 
40121 .03; 21 


22.11 21 
22.82 22 
23.54 23 
24.25 23 
24.1 
25.68 
26.39 
27. 10 
27.82 
28.53 

29.24 
29.96 
30.67 
31.38 
32.10 
32.81 
33.52 

34.24 
34.95 
35.66 



.24 32 
.94 33 
,64 34 
.34 34 
.05 35 


02 21 
73 22 
44! 23 
15123, 
,86124, 
, 57125, 
,28 26 
99 26 

27 

28 

28 

29 

30 

30 

31 

32 


82)21. 
53 22. 
23 23. 
34; 124. 
641,24. 
34 ;25. 


05 
75 
,46 
, 16 


92121. 
63 22. 
33 23. 
04 ; 24, 
75|24, 
46125, 
i26.l6|26, 
|26.87|26, 
i 27.58 1 27 


92 31 
63 32 
33 33 
04134 
75 35 
46136 
16 37 


87 

58 


28 
,86128 
,57!! 29 
. 27 130 
.98 31 


68 
38 

.38',33.09 
.09 33 


31 

32 

33 


.80 34 
.51 35 


.79 33 
.50j34 
.20H35 


Dep. Lat. Dep. | Lat. [1 Dep. 

-1 


45} Deg. 


.28^28. 

.99128” 

.70)29, 

.41130 

.11 31 

.82131 

.53132 

.23133 

.94 33 

.65134 

.36135 


38 

39 


8 40 


.99 

.70 

.41 

.11 


41 

42 

43 

44 


.82 45 
.53146 
.23,47 
.94148 


.65 

.36 


45} Deg. 


L&t. 


45 Deg. 


49 

50 
































































































































THAVEP.SE table. 


’Ji 


l/l 

r-t- 

P> 

44 Deg 


l 

44.'{ 

De 

S • 

D 

O 

CD 

Lat. 

Dep. 

Lat. 

Dep. 

51 

36 

.69 

35. 

43 

36 

.53 

35 

.59 

52 

37 

.41 

36. 

12 

37 

.25 

36 

.29 

53 

38 

.12 

38. 

82 

37 

.96 

36 

.98 

54 

38 

.84 

37. 

51 

38 

.68 

37 

.68 

of 

39 

.56 38. 

21 

39 

.40 

38 

.38 

50 

40 

.28 

38. 

90 

40 

.11 

39 

.08 

57 

41 

.00 

39. 

60 

40 

.83 

39 

.77 

58 

41 

.72 

40. 

29 

41 

.55 

40 

.47 

59 

42 

.44 

40. 

98 

42 

.26 

41 

.17 

60 

43 

.16 

41. 

68 

42 

.98 

41 

.87 

61 

43 

.88 

42. 

37 

43 

.69 

42 

.57 

62 

44 

.60 

43. 

07 

44 

.41 

43 

.26 

63 

45 

.32 

43. 

76 

45 

.13 

43 

.96 

64 

46 

.04 

44. 

46 

45 

.84 

44 

.66 

65 

46 

.76 

45. 

15 

46 

.56 

45 

.36 

66 

47 

,48 

45. 

85 

47 

.28 

46 

. 05 

67 

48 

.20 

46. 

54 

47 

.99 

46 

.75 

68 

48 

.92 

47. 

24 

48 

.71 

47 

.45 

69 

49 

.63 

47. 

93 

49 

.42 

48 

.15 

70 

50 

.35 

48. 

63 

50 

.14 

48 

.85 

71 

51 

.07 

49. 

32 

50 

.86 

49 

.54 

72 

51 

.79 

50. 

02 

51 

.57 

50 

.24 

73 

52 

.53 

50. 

71 

52 

.29 

50 

.94 

74 

53 

.23151. 

40 

53 

.01 

51 

.64 

75 

53 

. 95 

52. 

10 

53 

.72 

52 

.33 

76 54 

67(52. 

79 

54 

.44 

53 

.03 

77 

55 

.39 53. 

49 

55 

.16 

53 

.73 

78 

56 

.11 

54. 

18 

55 

.87 

54 

.43 

79 

56 

.83 

54. 

88 

56 

.59 

55 

.13 

80 

57 

.55 55. 

57 

57 

.30 

55 

.82 

81 

58 

.27 56. 

27 

58 

.02 

56 

.52 


82 

83 

84 

85 

86 

87 

88 

89 

90 


91 

92 

93 

94 

95 


08.99 56.96| 58.74 
59.71 57.66 59.45 
60.42,58.35|!60.17 
89 
60 


61.14 59.05 60.1 
6l.86 5° 74 II 6 I .1 


44^ Deg. 


Lat. [ Dep. 


36.38 35.75 


37.09 

37.80 

38.52 

39.23 

39.94 


36.45 
37.15 
37.85 
38.55 
39.25 


40.66 39.95 
41.37 40.65 
42.08 41.35 
42.79142.05 

43'..51 42 
44.22 

44.93 
45.05 
46.36 
47.07 
47.79 
48.50 
49.21 

49.93 


96 69 

97'69 
98170, 


100 71 


w 

V 

M 

ei . 


62.5S ( 6o. 
63.30(61, 
64.02 61. 
64.74 62. 

46 63. 
18 63 
90 64 
62 65 
34 65 
06 66 
78 67 
50 68 
21 68 
93 69 


65, 

66 , 
66 , 

67, 

68 . 


.91 

.60 

.30 

.99 

.69 

.38 

.08 

.77 

.47 




32(60 
03 61 


Dep. Lnt 


46 Deg. 


65, 

65, 

66 , 
167. 
68 , 
63. 
(69. 
70. 

70. 

71. 


18 

90 

62 

33 

05 

76 


83.50 
64.20 
64.89 
65.59 
66.29 
66.99 
48 67.69 
20 68.38 
91 69.08 
63 69.78 


Dep. Lat. 


45 f Des*. 


50.64 

51.35 
52.07 
52.78 
53.49 
54.21 
54.92 
55.63 

56.35 
57 .06 


57.77 
58.49 
59.20 
59.91 
60.63 
61.34 
62.05 

62.77 
63.48 
64.19 


64.91 

65.62 

66.33 
67.05 
67.76 
68.47 
69.19 
69.90 
70.61 

71.33 


Dep. 


.76 
43.46 
44.16 
44.86 
45.56 
46.26 
46.96 
47.68 
48.36 
49.06 


49.76 

50.47 

51.17 

51.87 

52.57 

53.27 

53.97 

54.67 

55.37 

56.07 


56.77 
57.47 
58.18 
58.88 
59.58 
60.2S 
60.98 
61.68 
62.38 
63.08 


63.78 

64.48 

65.18 

65.89 

66.59 

67.29 

67.99 

68.69 

69.39 

70.09 


Lat. 


45 i Deg. 


53.26 (52.80 
53.97 53.51 


54.68 


54.21 


55.39 54.91 
56.10 55.62 
56.81)56.32 

57.52 57.03 


58.24 
58.95 
59.66 
60.37 
61.08 


57.73 

58.43 

59.14 

59.84 

60.55 


44f De 


45 Deg 


C 

P 

Lat. 

Dep. 

L 

at. 

Dep. 

3 

O 

O 

36 

.22 

35 

.90 

36 

.06 

36. 

06 

51 

36 

.93 

36 

.61 

36 

.77 

36, 

77 

52 

37 

.64 

37 

.31 

37 

.48 

37. 

48 

53 

38 

.35 

38 

.02 

38 

.18 

38. 

18 

54 

39 

.06 

38 

.72' 

38 

.89 

38. 

89 

55 

39 

.77 

39 

.42 

39 

.60 

39. 

60 

56 

40 

.48 

40 

.13 

40 

.31 

40. 

31 

57 

41 

.19 

40 

.83 

41 

.01 

41. 

01 

58 

41 

.90 

41 

.54 

41 

.72 

41. 

72 

53 

42 

.61 

42 

.24( 

42 

.43 

42. 

43 

60 

43 

.32 

42 

.94) 

43 

.13 

43. 

13 

61 

44 

.03 

43 

• 65 

43 

.84 

43. 

84 

62 

44 

.74 

44 

.35' 

44 

.55 

44. 

55 

63 

45 

.45 

45 

.06 

45 

.25 

45. 

25 

64 

46 

.16 

45 

.76( 

45 

.96 

45. 

96 

65 

46 

.87 

46 

.46 

46 

.67 

46. 

67 

66 

47 

.58 

47 

. 17 

47 

.38 

47. 

38 

67 

48 

.29 

47 

.87 

48 

.08 

48. 

08 

58 

49 

.00 

48 

.58 

48 

.79 

48. 

79 

69 

49 

.71 

49 

.28 

49 

.50 

49. 

50 

70 

50 

.42 

49 

. 9S 

50 

.20 

50. 

20 

71 

51 

.13 

50 

.69 

50 

.91 

50. 

91 

72 

51 

.84 51 

.39 

51 

.62 

51. 

62 

73 

52 

.55 52 

.10 

52 

.33 

52. 

33 

74 


53.03 
53.74 
54.45 
55.15 
55.86 
56.57 56.57 

57.28 57.28 


53.03 

53.74 

54.45 

55.15 

55.86 


57.98 

58.69 

59.40 


57.98 
58.69 
59.40 


60.10(60.10 
60.81160.81 
'61.79 61.25; 61.52 61.52 
62.50 61.95 62.23 62.23 
[63.21 62.66 62.93 62.93 
63.92)63.36: 63.64 63.64 

64.63,64.07;[64.35 64.35 
(65.34 64.77 65.05(65.05 


66.05 

66.76 


65.47 

66.18 


67.47 66.88 
68.18 67.59 


68.89 

69.60 

70.31 

71.02 


Dep. 


68.29 

68.99 

69.70 

70.40 


Lat. 


45J Deg. 


05.76 65.76 
66.47)60.47 
67.18:67.18 
67.88 67.88 
68.59 68.59 
69.30 69.30 
70.00) 70.00 
70.71 70.71 


•75 

76 

77 

78 

79 

80 


81 

82 

83 

84 

85 

86 

87 

88 

89 

90 


Dep. 


Lat. 


45 Deg. 


91 

92 

93 

94 f 
951 
981 
9? 

98 

99 
300 










































































































































A TABLE OF RHUMBS 


SHOWING 

DEGREES, MINUTES, AND SECONDS, THAT EVERY POINT AND QUARTS S 
POINT OF TIIE COMPASS MAKES WITH 
THE MERIDIAN. 


NORTH. 

|Pts. 

qr 

o 

/ 

// 

1 Pts. 

qr 

SOOTH. 



0 

1 

2 

48 

45 

|0 

1 





1 

2 

5 

37 

30 

0 

2 





0 

3 

8 

26 

15 

0 

3 



N by E. 

N. by W. 

1 

0 

11 

15 

0 

1 

0 

S. by E. 

; S. by W. 



1 

1 

14 

3 

45 

1 

1 





1 

2 

16 

52 

30 

1 

2 





1 

3 

J 9 

41 

15 

1 

3 



N.N.E. 

N.N.W. 

2 

0 

22 

30 

0 

2 

0 

S.S.E. 

s.s.w 



2 

1 

25 

18 

45 

2 

1 





2 

2 

28 

7 

30 

2 

2 





2 

3 

30 

55 

15 

2 

3 



N.E.byN. 

N.W. by N. 

3 

0 

33 

45 

0 

3 

0 

S.E. by S. 

S.W. by S 



3 

1 

33 

33 

45 

3 

1 





3 

o 

44 

39 

22 

30 

3 

2 


t 



3 

3 

42 

11 

15 

3 

3 



N.E. 

N.W. 

4 

0 

45 

0 

0 

4 

0 

S.E. 

S.W 



4 

1 

47 

48 

45 

4 

1 





4 

2 

50 

37 

30 

4 

2 



N.E. byE. 


4 

3 

53 

26 

15 

4 

3 



N.W.by W. 

5 

0 

56 

15 

0 

5 

0 

S.E. byE. 

S.W. by W 



5 

1 

59 

3 

45 

5 

1 





5 

2 

61 

52 

30 

5 

2 



E.N.E, 


5 

3 

64 

41 

15 

5 

3 



W.N.W. 

6 

0 

67 

30 

0 

6 

0 

E.S.E. 

W S.W. 



6 

1 

70 

18 

45 

6 

1 





6 

2 

73 

7 

30 

6 

2 



E. by N 


6 

3 

75 

56 

15 

6 

3 



W. by N. 

7 

0 

78 

45 

0 

7 

0 

E. by S. 

W. by S 



7 

1 

81 

33 

45 

7' 

1 





7 


84 

22 

30 

7 

2 



JSsat. 


7 

3 

87 

11 

15 

7 

3 



West. 

8 

0| 

90 

0 

o! 

8 

0 

East. 

West. 

































WORKMAN S TABLE, FOR CORRECTING THE MIDDLE LATITUDE. 93 




Mid. 


Lat. 

1 

30 


40 


50 


60 

| 

70 


80 


90 


10 O 

| 

HO 

o 

c 

' 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

o 

/ 

15 

0 

02 

0 

03 

0 

04 

0 

00 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

16 

0 

02 

0 

03 

0 

04 

0 

00 

0 

09 

0 

12 

0 

15 

0 

18 

0 

22 

17 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

21 

18 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

20 

19 

0 

02 

0 

03 

0 

04 

0 

00 

0 

07 

0 

10 

0 

13 

0 

16 

0 

19 

29 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

21 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

22 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

17 

23 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

17 

24 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

25 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

20 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

27 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

08 

0 

11 

0 

14 

0 

10 

28 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

29 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

30 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

31 

0 

02 

0 

03 

0 

04 

0 

G5 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

32 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

33 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

34 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

35 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

30 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

37 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

38 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

39 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

40 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

41 

0 

02 

0 

03 

0 

04 

0 

05 

0 

08 

0 

03 

0 

10 

0 

13 

0 

15 

42 

0 

02 

0 

03 

0 

04 

0 

05 

0 

06 

0 

08 

0 

10 

0 

13 

0 

15 

43 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

44 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

10 

45 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

46 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

47 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

48 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

16 

49 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

50 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

51 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

11 

0 

14 

0 

17 

52 

0 

02 

0 

03 

0 

04 

0 

05 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

53 

0 

02 

0 

03 

0 

04 

0 

06 

0 

07 

0 

09 

0 

12 

0 

15 

0 

18 

54 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

16 

0 

19 

65 ! 

0 

02 

0 

03 

0 

04 

0 

06 

,0 

08 

0 

10 

0 

13 

0 

16 

0 

19 

56 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

16 

0 

20 

57 

0 

02 

0 

03 

0 

04 

0 

06 

0 

08 

0 

11 

0 

14 

0 

17 

0 

20 

58 

0 

02 

0 

03 

0 

04 

0 

06 

0 

09 

0 

11 

0 

14 

0 

17 

0 

21 

59 

0 

02 

0 

03 

0 

04 

0 

06 

0 

09 

0 

12 

0 

15 

0 

18 

0 

22 

60 

0 

02 

0 

03 

0 

04 

0 

00 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

61 

0 

02 

0 

03 

0 

05 

0 

07 

0 

09 

0 

12 

0 

15 

0 

19 

0 

23 

02 

0 

02 

0 

03 

0 

05 

0 

07 

0 

09 

0 

12 

0 

16 

0 

20 

0 

24 

03 

0 

02 

0 

04 

0 

05 

0 

07 

0 

09 

0 

13 

0 

16 

0 

20 

0 

24 

04 

0 

02 

0 

04 

0 

06 

0 

08 

0 

09 

0 

13 

0 

17 

0 

21 

0 

25 

65 | 

0 

02 

0 

04 

0 

06 

0 

08 

0 

10 

0 

13 

0 

17 

0 

21 

0 

25 

GO i 

0 

02 

0 

04 

0 

06 

0 

08 

0 

10 

0 

14 

0 

18 

0 

22 

0 

20 j 

fi7 1 

0 

02 

0 

04 

0 

06 

0 

08 

0 

11 

0 

15 

0 

18 

0 

23 

0 

27 1 

08 

0 

02 

0 

04 

0 

00 

0 

08 

0 

11 

0 

15 

0 

19 

0 

24 

0 

28 

09 

0 

02 

0 

05 

0 

06 

0 

09 

0 

12 

0 

16 

0 

20 

0 

25 

0 

30 

70 

0 

03 

0 

05 

0 

06 

0 

09 

0 

13 

0 

17 

0 

21 

0 

26 

0 

31 

71 

0 

04 

0 

00 

0 

07 

0 

09 1 

0 

13 

0 

18 

0 

22 

0 

27 

0 

33 

72 

0 

04 

0 

00 

0 

08 

0 

10 1 

0 

14 

0 

19 

0 

23 

0 

29 

0 

35 


25 









































94 WORKMAN’S TABLE, FOR CORRECTING THE MIDDLE T . ATITUDF. 


--■ 5 vjrjamaa 


Mid. 

Lat. 

120 

o 

CO 

rH 

140 


150 

160 

, 170 

1 180 

19° 

200 


o 

/ 

o 


o 

/ 

0 

/ 

o / 

o / 

0 

/ 

O / 

c 

/ 

15 

0 

27 

0 

31 

0 

35 

0 

40 

0 45 

0 51 

0 

58 

1 06 

1 

14 

16 

0 

26 

0 

30 

0 

34 

0 

38 

0 43 

0 49 

0 

56 

1 03 

1 

11 

17 

0 

25 

0 

28 

0 

32 

0 

37 

0 42 

0 48 

0 

54 

1 01 

1 

03 

18 

0 

24 

0 

27 

0 

31 

0 

36 

0 41 

0 46 

0 

52 

0 58 

1 

06 

19 

0 

23 

0 

26 

0 

30 

0 

34 

0 40 

0 45 

0 

50 

0 56 

1 

03 

20 

0 

22 

0 

25 

0 

29 

0 

33 

0 38 

0 43 

0 

48 

0 54 

\ 1 

00 

21 

0 

21 

0 

25 

0 

29 

0 

33 

0 37 

0 42 

0 

47 

0 53 

1 o 

58 

22 

0 

20 

0 

24 

0 

28 

0 

32 

0 36 

0 41 

0 

46 

0 51 

0 

56 

23 

0 

20 

0 

24 

0 

28 

0 

32 

0 36 

0 40 

0 

45 

0 50 

0 

55 

24 

0 

19 

0 

23 

0 

27 

0 

31 

0 35 

0 39 

0 

44 

0 48 

0 

53 

25 

0 

19 

0 

23 

0 

27 

0 

31 

0 35 

0 39 

0 

43 

0 47 

0 

52 

28 

0 

19 

0 

22 

0 

26 

0 

30 

0 34 

0 33 

0 

42 

0 47 

0 

52 

27 

0 

19 

0 

22 

0 

26 

0 

30 

0 33 

0 38 

0 

42 

0 46 

0 

51 

28 

0 

18 

0 

21 

0 

25 

0 

29 

0 33 

0 37 

0 

41 

0 46 

0 

51 

29 

0 

18 

0 

21 

0 

25 

0 

29 

0 32 

0 36 

0 

41 

0 45 

0 

50 

30 

0 

18 

0 

21 

0 

25 

0 

28 

0 32 

0 36 

0 

41 

0 45 

0 

50 

31 

0 

18 

0 

21 

0 

25 

0 

28 

0 32 

0 38 

0 

41 

0 45 

0 

50 

32 

0 

18 

0 

21 

0 

25 

0 

28 

0 31 

0 36 

0 

41 

0 45 

0 

50 

33 

0 

18 

0 

21 

0 

24 

0 

27 

0 31 

0 35 

0 

40 

0 44 

0 

49 

34 

0 

18 

0 

21 

0 

24 

0 

27 

0 31 

0 35 

0 

40 

0 41 

0 

49 

35 

0 

18 

0 

21 

0 

24 

0 

27 

0 31 

0 35 

0 

40 

0 44 

0 

49 

36 

0 

18 

0 

21 

0 

24 

0 

27 

0 31 

0 36 

0 40 

0 44 

0 

49 

37 

0 

18 

0 

21 

0 

24 

0 

27 

0 31 

0 35 

0 

40 

0 44 

0 

49 

38 

0 

18 

0 

21 

0 

24 

0 

27 

0 31 

0 36 

0 

40 

0 45 

0 

50 

39 

0 

18 

0 

21 

0 

25 

0 

28 

0 32 

0 36 

0 

41 

0 45 

0 

50 

40 

0 

18 

0 

22 

0 

25 

0 

28 

0 32 

0 36 

0 

41 

0 45 

0 

50 

41 

0 

18 

0 

22 

0 

25 

0 

28 

0 32 

0 37 

0 

41 

0 45 

0 

50 

42 

0 

18 

0 

22 

0 

26 

0 

29 

0 33 

0 37 

0 

42 

0 46 

0 

51 

43 

0 

19 

0 

23 

0 

26 

0 

30 

0 34 

0 38 

0 

42 

0 46 

0 

51 

44 

0 

19 

0 

23 

0 

27 

0 

30 

0 34 

0 3S 

0 

43 

0 47 

0 

52 

45 

0 

19 

0 

23 

0 

27 

0 

31 

0 35 

0 39 

0 

43 

0 47 

0 

52 

46 

0 

19 

0 

23 

0 

27 

0 

31 

0 35 

0 39 

0 

44 

0 48 

0 

53 

47 

0 

20 

0 

23 

0 

27 

0 

31 

0 35 

0 40 

0 

44 

0 49 

0 

54 

48 

0 

20 

0 

23 

0 

27 

0 

31 

0 35 

0 40 

0 

45 

0 50 

0 

55 

49 

0 

21 

0 

24 

0 

28 

0 

32 

0 36 

0 41 

0 

46 

0 51 

0 

67 

50 

0 

21 

0 

24 

0 

28 

0 

32 

0 36 

0 41 

0 

46 

0 52 

0 

58 

51 

0 

21 

0 

24 

0 

28 

0 

32 

0 37 

0 42 

0 

47 

0 53 

0 

59 

52 

0 

22 

0 

25 

0 

29 

0 

33 

0 37 

0 42 

0 

48 

0 54 

1 

00 

53 

0 

22 

0 

25 

0 

29 

0 

33 

0 38 

0 43 

0 

49 

0 55 

1 

01 

54 

0 

23 

0 

26 

0 

30 

0 

34 

0 39 

0 44 

0 

50 

0 50 

1 

02 

55 

0 

23 

0 

26 

0 

30 

0 

35 

0 40 

0 45 

0 

51 

0 57 

1 

03 

56 

0 

24 

0 

27 

0 

31 

0 

36 

0 41 

0 48 

0 

52 

0 58 

1 

04 

57 

0 

24 

0 

28 

0 

32 

0 

37 

0 42 

0 48 

0 

54 

1 00 

1 

06 

58 

0 

25 

0 

29 

0 

33 

0 

38 

0 44 i 

0 50 

0 

55 

1 02 

1 

08 

59 

9 

26 

0 

30 

0 

34 

0 

39 

0 45 1 

0 51 

0 

57 

1 01 

] 

10 

60 

0 

27 

0 

31 

0 

35 

0 

40 

0 46 

0 52 

0 

59 

1 06 

] 

13 

61 

0 

27 

0 

31 

0 

36 

0 

41 

0 47 

0 54 

1 

01 

1 08 

1 

15 

62 

0 

28 

0 

32 

0 

37 

0 

42 

0 49 

0 56 

1 

03 

1 10 

1 

18 

63 

0 

29 

0 

33 

0 

39 

0 

44 

0 51 

0 58 

1 

05 

1 12 

1 

21 

64 

0 

29 

0 

34 

0 

40 

0 

46 ! 

0 53 

1 00 

1 

07 

1 14 

1 

24 

65 

0 

30 

0 

35 

0 

41 

0 

48 I 

0 55 

1 02 

1 

09 

1 17 

1 

27 

66 

0 

31 

0 

37 

0 

43 

0 

50 

0 58 

1 05 

1 

12 

i 21 

1 

31 

67 

0 

33 

0 

38 

0 

45 

0 

53 

1 00 

1 07 

1 

16 

1 25 

1 

35 

68 

0 

34 

0 

40 

0 

48 

0 

55 

1 02 

1 10 

1 

19 

1 30 

1 

39 

69 

0 

36 

0 

42 

0 

50 

0 

58 

1 05 

1 13 

1 

23 

1 34 

1 

44 

70 

0 

38 

0 

44 

0 

52 

1 

00 

1 08 

1 17 

1 

28 

1 39 

1 

50 

71 

0 

40 

0 

46 

0 

55 

1 

03 

1 12 

1 22 i 

1 

32 

1 44 

1 

56 

72 1 

0 

42 

0 

49 

0 

58 

1 

06 

1 16 

1 27 | 

1 

38 

1 50 

o 

04 














































TABLE OF MERIDIONAL PARTS. 


95 


2 M, 

ewisr »r* 

p>yio 

20 

301 40 

5"oj 60 

70 

80 

. 901 10 o| no| i 20 | 130 

I 0 

0 

60 

120 

180 

240 

300 

361 

421 

482 

542 

603 

664 

725 

787 

1 

1 

61 

121 

181 

241 

301 

362 

422 

483 

543 

604 

665 

726 

788 

" o 

2 

62 

122 

182 

242 

302 

363 

423 

484 

544 

605 

666 

727 

789 

3 

3 

63 

123 

183 

243 

303 

364 

424 

485 

545 

606 

667 

728 

790 

4 

4 

64 

124 

184 

244 

304 

365 

425 

486 

546 

607 

668 

729 

791 

•5 

5 

65 

125 

185 

245 

305 

366 

426 

487 

547 

608 

669 

730 

7'92 

G 

6 

66 

126 

186 

246 

306 

367 

427 

488 

548 

609 

670 

731 

793 

7 

7 

67 

127 

187 

247 

307 

368 

428 

489 

549 

610 

671 

732 

794 

8 

8 

6 S 

128 

188 

248 

308 

369 

429 

490 

550 

611 

672 

734 

795 

9 

9 

69 

129 

189 

249 

309 

370 

430 

491 

551 

612 

673 

735 

796 

10 

10 

70 

130 

190 

250 

310 

371 

431 

492 

552 

613 

664 

736 

797 

11 

11 

71 

131 

191 

251 

311 

372 

432 

493 

553 

614 

675 

737 

798 

12 

12 

72 

132 

192 

252 

312 

373 

433 

494 

554 

615 

676 

73S 

799 

13 

13 

73 

133 

193 

253 

313 

374 

434 

495 

555 

616 

677 

739 

800 

14 

14 

74 

134 

194 

254 

314 

375 

435 

496 

556 

617 

678 

740 

801 

15 

15 

75 

135 

195 

255 

315 

376 

436 

497 

557 

6 • 6 

679 

741 

802 

16 

16 

76 

136 

196 

256 

316 

377 

437 

498 

558 

619 

680 

742 

803 

17 

17 

77 

137 

197 

257 

317 

378 

438 

499 

559 

620 

681 

743 

804 

18 

18 

78 

138 

198 

258 

318 

379 

439 

500 

560 

621 

682 

744 

805 

19 

19 

79 

139 

199 

259 

319 

380 

440 

501 

561 

622 

683 

745 

806 

20 

20 

80 

140 

200 

260 

320 

381 

441 

502 

562 

623 

684 

746 

807 

21 

21 

81 

141 

201 

261 

321 

382 

142 

503 

563 

624 

685 

747 

808 

22 

22 

82 

142 

202 

262 

322 

383 

443 

504 

564 

625 

687 

748 

809 

23 

23 

83 

143 

203 

263 

323 

384 

444 

505 

565 

626 

688 

749 

810 

24 

24 

84 

144 

204 

264 

324 

385 

445 

506 

567 

627 

689 

750 

811 

25 

25 

85 

145 

205 

265 

325 

386 

446 

507 

56S 

628 

690 

751 

812 

26 

26 

86 

146 

206 

266 

326 

387 

447 

508 

569 

629 

691 

752 

813 

27 

27 

87 

147 

207 

267 

327 

388 

448 

509 

570 

631 

G92 

753 

815 

28 

28 

88 

148 

208 

268 

328 

389 

449 

510 

571 

632 

693 

754 

816 

29 

29 

89 

149 

209 

269 

330 

390 

450 

511 

572 

633 

694 

755 

817 

30 

30 

90 

150 

210 

270 

331 

391 

451 

512 

rr 

5/3 

634 

695 

756 

818. 

31 

31 

91 

151 

211 

271 

332 

392 

452 

513 

r.74 

t) t n 

635 

696 

757 

819 

32 

32 

92 

152 

212 

272 

333 

393 

453 

514 

575 

636 

697 

758 

820 

33 

33 

93 

153 

213 

273 

334 

394 

454 

515 

576 

637 

698 

759 

821 

34 

34 

94 

154 

214 

274 

335 

395 

455 

516 

577 

638 

699 

760 

822 

35 

35 

95 

155 

215 

275 

336 

396 

456 

517 

578 

639 

700 

761 

823 

30 

36 

96 

156 

216 

276 

337 

397 

457 

518 

579 

640 

701 

762 

824 

37 

37 

97 

157 

217 

277 

338 

398 

458 

519 

590 

641 

702 

763 

825 

38 

38 

98 

158 

218 

278 

339 

399 

459 

520 

581 

642 

703 

764 

826 

39 

39 

93 

159 

219 

279 

340 

400 

460 

521 

582 

643 

704 

765 

827 

40 

40 

100 

160 

220 

280 

341 

401 

461 

522 

583 

644 

705 

766 

823 

41 

41 

101 

161 

221 

281 

342 

402 

462 

523 

584 

645 

706 

767 

829 

42 

42 

102 

162 

222 

282 

343 

403 

463 

524 

585 

646 

707 

768 

830 

43 

43 

103 

163 

223 

283 

344 

404 

464 

525 

586 

647 

708 

769 

831 

44 

44 

104 

164 

224 

284 

345 

405 

465 

526 

587 

648 

709 

770 

832 

45 

45 

105 

165 

225 

285 

346 

406 

466 

527 

588 

649 

710 

771 

833 

46 

46 

108 

166 

226 

286 

347 

407 

467 

528 

589 

650 

711 

772 

834 

47 

47 

107 

167 

227 

287 

348 

408 

468 

529 

590 

651 

712 

773 

S35 

48 

48 

108 

168 

228 

288 

349 

409 

469 

530 

591 

652 

713 

774 

S36 

49 

49 

109 

169 

229 

289 

350 

410 

470 

531 

592 

653 

714 

775 

837 

50 

50 

110 

170 

230 

290 

351 

411 

471 

532 

593 

654 

715 

777 

838 

51 

51 

111 

171 

231 

291 

352 

412 

472 

533 

594 

655 

716 

778 

839 

52 

52 

112 

172 

232, 

292 

353 

413 

473 

534 

595 

656 

717 

779 

840 

53 

53 

113 

173 

233 

293 

354 

414 

474 

535 

596 

657 

718 

780 

841 

54 

54 

114 

174 

234 

294 

355 

415 

476 

536 

597 

65S 

719 

781 

842 

55 

55 

115 

175 

235 

295 

356 

416 

477 

537 

598 

659 

720 

782 

843 

56 

56 

116 

176 

236 

296 

357 

417 

478 

538 

599 

660 

721 

783 

844 

57 

57 

117 

177 

237 

297 

358 

418 

479 

539 

600 

661 

722 

784 

845 

58 

58 

118 

178 

238 

238 

359 

419 

480 

540 

601 

662 

723 

785 

846 

59 

59 

119 

179 

239 

■rvxst 

299 

360 

420 

481 

541 

602 

663 

U.S13IBXX 

724 

«ci\3=cnnrjH 

786 

847 
















































96 


TABLE OF MERIDIONAL PARTS, 


*M. j 140| 150| 160| I70| 18Q| i9oj 20o| 21o| 22Q| 230] 24oj 250] 260) 270 


0 

848 

910 

973 

1035 

1098 

1161 

1225 

1289 

1354 

1419 

1484 

1550 

1616 

1684 

1 

850 

911 

974 

36 

99 

63 

26 

90 

55 

20 

85 

51 

18 

85 

2 

851 

913 

975 

37 

1100 

64 

27 

91 

56 

21 

86 

52 

19 

86 

3 

852 

914 

976 

38 

01 

65 

28 

92 

57 

22 

87 

53 

20 

87 

4 

853 

915 

977 

39 

02 

66 

29 

93 

58 

23 

88 

54 

21 

88 

5 

854 

916 

978 

41 

03 

67 

30 

95 

59 

24 

90 

56 

22 

89 

6 

855 

917 

979 

42 

05 

68 

32 

96 

60 

25 

91 

57 

23 

90 

7 

856 

918 

980 

43 

06 

69 

33 

97 

61 

26 

92 

58 

24 

91 

8 

857 

919 

981 

44 

07 

70 

34 

98 

62 

27 

93 

59 

25 

93 

9 

858 

920 

982 

45 

08 

71 

35 

99 

63 

28 

94 

60 

26 

94 

10 

859 

921 

983 

1046 

1109 

1172 

1236 

1300 

1364 

1430 

1495 

1561 

1628 

1695 

11 

860 

922 

984 

47 

10 

73 

37 

01 

66 

31 

96 

62 

29 

96 

12 

861 

923 

985 

48 

11 

74 

38 

02 

67 

32 

97 

63 

30 

97 

13 

862 

924 

986 

49 

12 

75 

39 

03 

68 

33 

98 

64 

31 

98 

14 

863 

925 

987 

50 

13 

76 

40 

04 

69 

34 

99 

65 

32 

99 

15 

864 

926 

988 

51 

14 

77 

41 

05 

70 

35 

1500 

67 

33 

1700 

10 

865 

927 

989 

52 

15 

78 

42 

06 

71 

36 

02 

68 

34 

01 

17 

866 

928 

990 

53 

16 

79 

43 

07 

72 

37 

03 

69 

35 

03 

18 

867 

929 

991 

54 

17 

81 

44 

08 

73 

38 

04 

70 

37 

04 

19 

868 

930 

993 

55 

18 

82 

45 

10 

74 

39 

05 

71 

38 

05 

20 

869 

931 

994 

1056 

1119 

1183 

1246 

1311 

1375 

1440 

1506 

1572 

1639 

1706 

21 

870 

932 

995 

57 

20 

84 

4S 

12 

76 

41 

07 

73 

40 

07 

22 

871 

933 

996 

58 

21 

85 

49 

13 

77 

43 

08 

74 

41 

08 

23 

872 

934 

997 

59 

22 

86 

50 

14 

79 

44 

09 

75 

42 

09 

24 

873 

935 

998 

60 

23 

87 

51 

15 

80 

45 

10 

77 

43 

11 

25 

874 

936 

999 

61 

25 

88 

52 

16 

81 

46 

11 

78 

44 

12 

26 

875 

937 

1000 

63 

26 

89 

53 

17 

82 

47 

13 

79 

45 

13 

27 

876 

938 

1001 

64 

27 

90 

54 

18 

83 

48 

14 

80 

47 

14 

28 

877 

939 

1002 

65 

28 

91 

55 

19 

84 

49 

15 

81 

48 

15 

29 

878 

941 

1003 

66 

29 

92 

56 

20 

85 

50 

16 

82 

49 

16 

30 

879 

942 

1004 

1067 

1130 

1193 

1257 

1321 

1386 

1451 

1517 

1583 

1650 

1717 

31 

880 

943 

05 

6 S 

31 

94 

58 

22 

87 

52 

18 

84 

51 

18 

32 

882 

944 

06 

69 

32 

95 

59 

24 

88 

53 

19 

85 

52 

20 

33 

883 

945 

07 

70 

33 

96 

60 

25 

89 

55 

20 

86 

53 

21 

34 

884 

946 

08 

71 

34 

98 

61 

26 

90 

56 

21 

88 

54 

22 

35 

885 

947 

09 

72 

35 

99 

62 

27 

92 

57 

22 

89 

56 

23 

36 

886 

948 

10 

73 

36 

1200 

64 

28 

93 

58 

24 

90 

57 

24 

37 

887 

949 

11 

74 

37 

01 

65 

29 

94 

59 

25 

91 

58 

25 

38 

888 

950 

12 

75 

38 

02 

66 

30 

95 

60 

26 

92 

59 

26 

39 

889 

951 

13 

76 

39 

03 

67 

31 

96 

61 

27 

93 

60 

27 

40 

890 

952 

1014 

1077 

1140 

1204 

J26S 

1332 

1397 

1462 

1528 

1594 

1661 

1729 

41 

891 

953 

15 

78 

41 

05 

69 

33 

98 

63 

29 

96 

62 

30 

42 

892 

954 

16 

79 

42 

06 

70 

34 

99 

64 

30 

97 

63 

31 

43 

893 

955 

18 

80 

44 

07 

71 

35 

1400 

65 

31 

98 

64 

32 

44 

894 

956 

19 

81 

45 

08 

72 

36 

01 

67 

32 

99 

66 

33 

45 

895 

957 

20 

82 

46 

09 

73 

38 

02 

68 

33 

1600 

67 

34 

46 

896 

958 

21 

84 

47 

10 

74 

39 

03 

69 

35 

01 

68 

35 

47 

897 

959 

22 

85 

48 

11 

75 

40 

05 

70 

36 

02 

69 

36 

48 

898 

960 

23 

86 

49 

12 

76 

41 

06 

71 

37 

03 

70 

38 

49 

899 

961 

24 

87 

50 

13 

77 

42 

07 

72 

38 

04 

71 

39 

50 

900 

962 

1025 

10 S8 

1151 

1215 

1278 

1343 

1408 

1473 

1539 

1605 

1672 

; 740 

51 

901 

963 

26 

89 

52 

16 

80 

44 

09 

74 

40 

06 

73 

41 

52 

902 

964 

27 

90 

53 

17 

81 

45 

10 

75 

41 

08 

75 

42 

53 

903 

965 

28 

91 

54 

18 

82 

46 

11 

76 

42 

09J 76 

13 

54 

904 

966 

29 

92 

55 

19 

83 

47 

12 

77 

43 

10 

77 

44 

55 

905 

968 

30 

93 

56 

20 

84 

4S 

13 

79 

44 

11 

78 

46 

56 

906 

969 

31 

94 

57 

21 

85 

49 

14 

80 

46 

1 12 

79 

47 

57 

907 

970 

32 

95 

58 

22 

86 

50 

15 

81 

47 

13 

80 

48 

58 

908 

971 

33 

96 

59 

23 

87 

52 

16 

82 

48 

14 

81 

49 

59 

909 

972 

34 

97 

60 

0/1 

a,* 

88 

53 

18 

I 83 

1 49 

15 

82 

50 











































TABLE OF MERIDIONAL PARTS. 


9 ? 


M;j^8of29of30oj 31o| 320) 3301 340j"35oi T$0o| :37oj '38o'j""39oj 40o[" 4l'o 


0 

1751 

1819 

1888 

1958 

2028 

2100 

2171 

2244 2318 

239312468 

2545 

2623 

2702 

. 1 

52 

21 

90 

59 

30 

01 

73 

46 

19 

94 

70 

46 

24 

03 

2 

53 

22 

91 

60 

31 

02 

74 

47 

20 

95 

71 

48 

25 

04 

3 

55 

23 

92 

62 

32 

33 

75 

48 

22 

96 

72 

49 

27 

06 

1 

56 

24 

93 

63 

33 

04 

76 

49 

23 

98 

73 

50 

28 

07 

5 

57 

25 

94 

64 

34 

05 

78 

50 

24 

99 

75 

51 

29 

08 

6 

58 

26 

95 

65 

35 

07 

79 

52 

25 

2400 

76 

53 

31 

10 

7 

59 

27 

96 

66 

37 

08 

80 

53 

27 

01 

77 

54 

32 

11 

8! GO 

29 

98 

67 

38 

09 

81 

54 

28 

03 

78 

55 

33 

12 

9 

61 

30 

99 

69 

39 

10 

82 

55 

29 

04 

80 

57 

34 

14 

10 

1762 

1831 

1900 

1970 

2040 

2111 

2184 

2257 

2330 

2405 

2481 

2558 

2636 

2715 

11 

64 

32 

01 

71 

41 

13 

85 

58 

32 

06 

82 

59 

37 

16 

12 

65 

33 

02 

72 

43 

14 

86 

59 

33 

08 

84 

60 

38 

18 

13 

66 

34 

03 

73 

44 

15 

87 

60 

34 

09 

85 

62 

40 

19 

14 

07 

35 

05 

74 

45 

16 

88 

61 

35 

10 

86 

63 

41 

20 

15 

68 

37 

06 

76 

46 

17 

90 

63 

37 

11 

*87 

64 

42 

22 

16 

69 

38 

07 

77 

47 

19 

91 

64 

38 

13 

89 

66 

44 

23 

17 

70 

39 

08 

78 

48 

20 

92 

65 

39 

14 

90 

67 

45 

24 

18 

72 

40 

09 

79 

50 

21 

93 

66 

40 

15 

91 

68 

46 

26 

19 

73 

41 

10 

80 

51 

22 

94 

68 

42 

16 

92 

69 

48 

27 

20 

1774 

1842 

1912 

1981 

2052 

2123 

2196 

2269 

2343 

2418 

2494 

2571 

2649 

2728 

21 

75 

43 

13 

83 

53 

25 

97 

70 

44 

19 

95 

72 

50 

29 

22 

76 

45 

14 

84 

54 

28 

98 

71 

45 

20 

96 

73 

51 

31 

23 

77 

46 

15 

85 

56 

27 

99 

72 

46 

22 

98 

75 

53 

32 

24 

78 

47 

16 

86 

57 

28 

2200 

74 

48 

23 

99 

76 

54 

33 

25 

80 

48 

17 

87 

58 

29 

02 

75 

49 

24 

2500 

77 

55 

35 

20 

81 

49 

18 

88 

59 

31 

03 

76 

50 

25 

01 

78 

57 

36 

27 

82 

50 

20 

90 

60 

32 

04 

77 

51 

27 

03 

80 

58 

37 

28 

83 

52 

21 

91 

61 

33 

05 

79 

53 

28 

04 

81 

59 

39 

29 

84 

53 

22 

92 

63 

34 

07 

80 

54 

29 

05 

82 

61 

40 

30 

1785 

1854 

1923 

1993 

2064 

2135 

2208 

2281 

2355 

2430 

2506 

2584 

2662 

2742 

31 

86 

55 

24 

94 

65 

37 

09 

82 

56 

32 

OS 

85 

63 

43 

32 

87 

56 

25 

95 

66 

38 

10 

83 

58 

33 

09 

86 

65 

44 

33 

89 

57 

27 

97 

67 

39 

11 

85 

59 

34 

10 

88 

66 

46 

34 

90 

58 

28 

98 

69 

40 

13 

86 

60 

35 

12 

89 

■ 67 

47 

35 

91 

60 

29 

99 

70 

41 

14 

87 

61 

37 

13 

90 

69 

48 

30 

92 

61 

30 

2000 

71 

43 

15 

88 

63 

38 

14 

91 

70 

50 

37 

93 

62 

31 

01 

72 

44 

16 

90 

64 

39 

15 

93 

71 

51 

38 

94 

63 

32 

02 

73 

45 

17 

91 

65 

40 

17 

94 

73 

52 

39 

95 

64 

34 

04 

75 

46 

19 

92 

66 

42 

18 

95 

74 

54 

40 

1797 

1865 

1935 

2005 

2076 

2147 

2220 

2293 

2368 

2443 

2519 

2597 

2675 

2755 

41 

98 

66 

36 

06 

77 

49 

21 

95 

69 

44 

21 

98 

76 

56 

42 

99 

68 

37 

07 

78 

50 

22 

96 

70 

45 

22 

99 

78 

58 

43 

1800 

69 

38 

08 

79 

51 

24 

97 

71 

47 

23 

2600 

79 

59 

44 

01 

70 

39 

10 

80 

52 

25 

98 

73 

48 

24 

02 

80 

60 

45 

02 

71 

41 

11 

82 

53 

26 

99 

74 

49 

26 

03 

82 

62 

46 

03 

72 

42 

12 

83 

55 

27 

2301 

75 

51 

27 

04 

83 

63 

47 

05 

73 

43 

13 

84 

56 

28 

02 

76 

52 

28 

06 

84 

64 

48 

06 

75 

44 

14 

85 

57 

30 

03 

78 

53 

30 

07 

86 

66 

49 

07 

76 

45 

15 

86 

58 

31 

04 

79 

54 

31 

08 

87 

67 

50 

1S08 

1877 

1946 

2017 

2088 

2159 

2232 

2306 

2380 

2456 

2532 

2G10 

2688 

2768 

51 

09 

78 

48 

18 

89 

61 

33 

07 

81 

57 

33 

11 

90 

70 

52 

10 

79 

49 

19 

90 

62 

35 

08 

83 

58 

35 

12 

91 

71 

63 

11 

80 

50 

20 

91 

63 

36 

09 

84 

59 

36 

14 

92 

72 

54 

13 

81 

51 

21 

92 

64 

37 

11 

85 

61 

37 

15 

94 

74 

55 

14 

83 

52 

22 

94 

65 

38 

12 

86 

62 

38 

16 

95 

10 

50 

15 

84 

53 

24 

95 

67 

39 

13 

88 

63 

40 

17 

96 

76 

57 

10 

85 

55 

25 

96 

68 

41 

14 

89 

64 

41 

19 

98 

78 

58 

17 

86 

56 

26 

97 

69 

42 

16 

90 

66 

42 

20 

99 

79 

59 

IS 

wwiownarai 

87 

57 

27 

98 

KaK -iEC0a.Kcn 

.70 

43 

17 

91 

67 

omausar--.* Jr 

44 

21 

UUKU1> 

12700 

80 

















































98 


TABLE OF MERIDIONAL FARTS. 


M. 

420 

430 

440j 

450j 4601 

470 

4801 

49°j 

50° 

510| 5201 

53°( 540 

550 

0 

2782 2S63 

2946 

3030 

3116 

3203 

329213382 

3474 

3569 

3665 

3764 

3865 

3988 

1 

83 

64 

47 

31 

17 

04 

93 

84 

76 

70 

67 

65 

67 

70 

2 

84 

66 

49 

33 

18 

06 

95 

85 

78 

72 

68 

67 

68 

71 

3 

86! 67 

50 

34 

20 

07 

96 

87 

79 

74 

70 

69 

70 

73 

4 

87 

69 

51 

36 

21 

09 

98 

88 

81 

75 

72 

70 

n 

75 

5 

88 

70 

53 

37 

23 

10 

99 

90 

82 

77 

73 

72 

73 

77 

f> 

90 

71 

54 

3S 

24 

12 

3301 

91 

84 

78 

75 

74 

75 

78 

7 

91 

73 

56 

40 

26 

13 

02 

93 

85 

80 

77 

75 

77 

80 

8 

92 

74 

57 

41 

27 

14 

03 

94 

87 

82 

78 

77 

78 

82 

9 

94 

75 

58 

43 

29 

16 

05 

96 

88 

83 

80 

79 

80 

84 

10 

2795 

2877 

2960 

3044 

3130 

3217 

3306 

3397 

3490 

3585 

3681 

37'80 

3882 

3985 

11 

97 

78 

61 

46 

31 

19 

08 

99 

92 

86 

83 

82 

83 

87 

12 

98 

80 

63 

47 

33 

20 

09 

3400 

93 

88 

85 

84 

85 

89 

13 

99 

81 

64 

48 

34 

22 

11 

02 

95 

90 

86 

85 

87 

91 

14 

2801 

82 

65 

50 

36 

23 

12 

03 

96 

91 

88 

87 

89 

92 

15 

02 

84 

67 

51 

37 

25 

14 

05 

98 

93 

90 

89 

90 

94 

16 

03 

85 

68 

53 

39 

26 

16 

07 

99 

94 

91 

90 

92 

96 

17 

05 

86 

70 

54 

40 

28 

17 

08 

3501 

96 

93 

92 

94 

98 

18 

06 

88 

71 

55 

42 

29 

19 

10 

03 

991 

95 

94 

95 

99 

19 

07 

89 

72 

57 

43 

31 

20 

11 

04 

99 

96 

95 

97 

4001 

20 

2809 

2891 

2974 

3058 

3144 

3232 

3322 

3413 

3506 

3601 

3698 

3797 

3899 

4003 

21 

10 

92 

75 

60 

46 

34 

24 

14 

07 

02 

99 

99 

39 J1 

05 

22 

11 

93 

76 

61 

47 

35 

25 

16 

09 

04 

3701 

3800 

02 

06 

23 

13 

95 

78 

63 

49 

37 

26 

17 

10 

06 

03 

02 

04 

08 

24 

14 

96 

79 

64 

50 

38 

23 

19 

12 

07 

(14 

04 

08 

10 

25 

15 

97 

81 

65 

52 

40 

29 

20 

14 

09 

06 

06 

07 

12 

26 

17 

99 

82 

67 

53 

41 

31 

22 

15 

10 

07 

07 

09 

14 

27 

18 

2900 

83 

68 

55 

42 

32 

23 

17 

12 

09 

09 

11 

15 

28 

20 

02 

85 

70 

58 

44 

34 

25 

18 

14 

If 1 

11 

13 

17 

29 

21 

03 

86 

71 

57 

45 

35 

27 

20 

15 

13 

12 

14 

19 

30 

2822 

2904 

2938 

3073 

3159 

3247 

3337 

3428 

3521 

3617 

3714 

3814 

3916 

4021 

31 

24 

06 

89 

74 

60 

48 

38 

30 

23 

18 

16 

16 

18 

22 

32 

25 

07 

91 

75 

62 

50 

40 

31 

25 

20 

17 

17 

19 

24 

33 

26 

08 

92 

77 

63 

51 

41 

33 

26 

22 

19 

19 

21 

26 

34 

28 

10 

93 

7S 

65 

53 

43 

34 

28 

23 

21 

21 

22 

28 

35 

29 

11 

95 

80 

66 

54 

44 

36 

29 

25 

22 

22 

25 

29 

36 

30 

13 

96 

81 

68 

56 

46 

37 

31 

26 

24 

24 

26 

31 

37 

32 

14 

99 

83 

69 

57 

47 

39 

32 

28 

26 

26 

28 

33 

38 

33 

15 

99 

84 

71 

59 

49 

40 

34 

30 

27 

27 

30 

35 

39 

34 

17 

3000 

85 

72 

60 

50 

42 

36 

31 

29 

29 

32 

37 

40 

2836 

2918 

3002 

3087 

3173 

3262 

3352 

344-3 

3537 

3633 

3731 

3831 

3933 

4038 

41 

37 

19 

03 

88 

75 

63 

53 

45 

39 

34 

32 

32 

35 

40 

42 

39 

21 

05 

90 

76 

65 

55 

47 

40 

36 

34 

34 

37 

42 

43 

40 

22 

06 

91 

78 

66 

56 

48 

42 

38 

36 

36 

38 

44 

44 

41 

24 

07 

93 

79 

68 

58 

50 

43 

39 

37 

39 

40 

45 

45 

43 

25 

09 

94 

81 

69 

59 

51 

45 

41 

39 

39 

42 

47 

46 

44 

26 

10 

95 

82 

71 

61 

53 

47 

43 

41 

41 

44 

49 

47 

45 

28 

12 

97 

84 

72 

62 

54 

49 

44 

42 

43 

45 

51 

48 

47 

29 

13 

98 

85 

74 

64 

56 

50 

46 

44 

44 

47 

52 

49 

48 

31 

14 

3100 

87 

75 

65 

57 

51 

47 

46 

46 

49 

54 

50 

2849 

2932 

3016 

3101 

3188 

3277 

3367 

3459 

3553 

3649 

3747 

3818 

3951 

4056 

51 

51 

33 

17 

03 

90 

78 

68 

60 

55 

51 

49 

49 

52 

58 

52 

52 

35 

19 

04 

91 

80 

70 

62 

56 

52 

50 

51 

54 

60 

53 

54 

36 

20 

05 

92 

81 

71 

64 

58 

54 

52 

53 

56 

61 

54 

55 

37 

21 

07 

94 

83 

73 

65 

59 

55 

54 

54 

58 

63 

55 

56 

39 

23 

08 

95 

84 

74 

67 

61 

57 

55 

56 

59 

65 

56 

58 

40 

24 

10 

97 

86 

76 

68 

62 

59 

57 

58 

61 

67 

57 

59 

42 

26 

11 

I 98 

87 

78 

70 

64 

60 

59 

60 

63 

69 

58 

60 

43 

27 

13 3200 

89 

79 

71 

66 

62 

60 

61 

64 

70 

59 

62 

44 

29 

14 I 01 

90 

81 

73 

67 

64-1 621 63 

66 72 






















































TABLE OP MERIDIONAL PARTS. 


D a 


M. I 56Q| 5?Pj 58Qj 59Q|'GQojeT^ 62Qj6P|^40|^of660| G7o]"o3o 


0 :J 


0 4074 

4183 

4294 

4409 

4527 

4649 

4775 

490515039 5179 

5324 

5474 

5651 

o / 0 

1 

76 

84 

96 

11 

29 

51 

77 

07 

42 

81 

26 

77 

33 

97 

2 

77 

86 

98 

13 

31 

53 

79 

09 

44 

84 

28 

79 

36 

5800 

3 

79 

88 

4300 

15 

33 

55 

81 

12 

46, 86 

31 

82 

33 

03 

4 

81 

90 

02 

17 

35 

57 

84 

14 

49 

88 

33 

84 

12 

06 

5 

83 

92 

04 

19 

37 

60 

86 

16 

r, » 

91 

36 

87 

44 

09 

6 

85 

94 

00 

21 

39 

62 

88 

18 

53 

93 

38 

89 

47 

11 

7 

86 

95 

08 

23 

41 

64 

90 

20 

55 

95 

41 

92 

50 

l-i 

8 

88 

97 

09 

25 

43 

66 

92 

23 

58 

98 

43 

95 

52 

17 

9 

90 

99 

11 

27 

45 

68 

94 

25 

60 5200 

46 

97 

55 

20 

10 4092 

4201 

4313 

4429 

4547 

4670 

4796 

4927 

5062 5203 

5348 

5500 

5658 

5823 

11 

94 

03 

15 

31 

49 

72 

98 

29 

65 

05 

51 

02 

60 

25 

12 

95 

05 

17 

33 

51 

74 

4801 

31 

67 

07 

53 

05 

63 

23 

13 

. 97 

07 

19 

34 

53 

76 

03 

34 

69 

10 

56 

07 

66 

31 

14 

99 

08 

21 

36 

55 

78 

05 

36 

71 

12 

58 

10 

68 

34 

15 

4101 

10 

23 

38 

57 

80 

07 

38 

74 

14 

61 

13 

rv i 

«i 

37 

16 

03 

12 

25 

40 

59 

82 

09 

40 

76 

17 

63 

15 

74 

39 

i T 

04 

14 

27 

42 

62 

84 

11 

43 

78 

19 

66 

18 

76 

42 

18 

06 

16 

28 

44 

64 

87 

14 

45 

81 

22 

68 

20 

79 

45 

19 

08 

18 

30 

46 

66 

89 

16 

47 

83 

24 

71 

23 

82 

48 

20 

4110 

4220 

4332 

4448 

4568 

4691 

4818 

4949 

5085 

5226 

5373 

5526 

5685 

5851 

21 

12 

21 

34 

50 

70 

93 

20 

51 

88 

29 

76 

28 

87 

54 

22 

13 

23 

36 

52 

72 

95 

22 

54 

90 

31 

78 

31 

90 

56 

23 

15 

25 

38 

54 

74 

97 

24 

56 

92 

34 

80 

33 

93 

59 

24 

17 

27 

40 

56 

76 

99 

26 

58 

95 

36 

83 

36 

95 

62 

25 

19 

29 

42 

58 

78 

4701 

29 

60 

97 

38 

85 

39 

98 

65 

28 

21 

31 

44 

60 

80 

03 

31 

63 

99 

41 

88 

41 

5701 

68 

27 

22 

32 

46 

62 

82 

05 

33^ 

65 

5102 

43 

90 

44 

04 

71 

28 

24 

34 

47 

64 

84 

07 

35 

67 

04 

46 

93 

46 

06 

74 

29 

26 

36 

49 

66 

86 

10 

37 

69 

06 

48 

95 

49 

09 

76 

30 

4128 

4238 

4351 

4468 

4588 

4712 

4839 

4972 

5108 

5250 

5338 

5552 

5712 

5879 

31 

30 

40 

53 

70 

90 

14 

42 

74 

11 

53 

5401 

54 

15 

82 

32 

32 

42 

55 

72 

92 

16 

44 

76 

13 

55 

03 

57 

17 

85 

33 

33 

44 

57 

74 

94 

18 

46 

78 

15 

58 

06 

59 

20 

88 

34 

35 

46 

59 

76 

96 

20 

48 

81 

18 

60 

08 

62 

23 

91 

35 

37 

47 

61 

78 

98 

22 

50 

83 

20 

63 

11 

65 

25 

94 

38 

39 

49 

63 

80 

4600 

24 

52 

85 

22 

65 

13 

67 

28 

98 

37 

41 

51 

65 

82 

02 

26 

55 

87 

25 

67 

1G 

70 

31 

99 

38 

42 

53 

67 

84 

04 

28 

57 

90 

27 

70 

18 

73 

34 

5902 

39 

44 

55 

69 

86 

06 

31 

59 

92 

29 

72 

21 

75 

36 

05 

40 

4146 

4257 

4370 

4488 

4608 

4733 

4861 

4994 

5132 

5275 

5423 

5578 

5739 

5908 

41 

48 

59 

72 

90 

10 

35 

63 

96 

34 

77 

26 

80 

42 

11 

42 

50 

60 

74 

92 

12 

37 

65 

99 

36 

80 

28 

83 

45 

14 

43 

52 

62 

76 

94 

14 

39 

68 

5001 

39 

82 

31 

86 

47 

17 

44 

53 

64 

78 

95 

16 

41 

70 

03 

41 

84 

33 

88 

50 

19 

45 

55 

66 

80 

97 

18 

43 

72 

05 

43 

87 

36 

91 

53 

22 

46 

57 

68 

82 

99 

20 

45 

74 

08 

46 

89 

38 

94 

56 

25 

47 

59 

70 

84 

4501 

23 

47 

76 

10 

48 

92 

41 

96 

58 

28 

48 

61 

72 

86 

03 

25 

50 

79 

12 

51 

94 

43 

99 

61 

31 

49 

62 

74 

88 

05 

27 

52 

81 

14 

53 

97 

46 

5602 

64 

34 

50 

4164 

1275 

4390 

4507 

4629 

4754 

4883 

5017 

5155 

5299 

5448 

5604 

5767 

5937 

51 

66 

77 

92 

09 

31 

56 

85 

19 

58 

5301 

51 

07 

70 

40 

52 

68 

79 

94 

11 

33 

58 

87 

21 

60 

04 

54 

10 

72! 43 

53 

79 

81 

96 

13 

35 

60 

90 

23 

62 

06 

56 

12 

75 

46 

54 

72 

83 

98 

15 

37 

62 

92 

26 

65 

09 

59 

15 

78 

18 

55 

73 

85 

99 

17 

39 

64 

94 

28 

67 

11 

61 

17 

81 

51 

56 

75 

87 

4401 

19 

41 

66 

96 

30 

69 

14 

64 

20 

83 

54 

57 

77 

89 

03 

21 

43 

69 

98 

33 

72 

16 

66 

23 

86 

57 

58 

79 

91 

05 

23 

45 

71 

4901 

35 

74 

19 

69 

25 

89 

60 

59 

81 

92 

07 

25 

47 

73 

03 

37 

76 

21 

71 

28 

92, 

63 











































10G 


TABLE OF MERIDIONAL PARTS. 


M.| 7001 7101 7201 730) 74-01 75©| 760) 77Q| 78Q| 79Q| 8QO| 81Q| 82Q| 83oj 


015966 6146 

6335 

6534 

6746 

6970 

7210 

7467 

7745 

8046 

8375 

8739 

9145 

9606 

1 

65, 49 

38 

38 

49 

74 

14 

72 

49 

51 

81 

45 

53 

14 

O 

72 

52 

41 

41 

53 

78 

18 

76 

54 

56 

87 

52 

60 

22 

Q 

0 

75 

55 

45 

45 

57 

82 

22 

81 

59 

61 

93 

58 

67 

31 

4 

78 

58 

48 

48 

60 

86 

27 

85 

64 

67 

98 

65 

74 

39 

5 

81 

61 

51 

52 

64 

90 

31 

90 

69 

72 

8404 

71 

82 

47 

6 

84 

64 

54 

55 

68 

94 

35 

94 

74 

77 

10 

78 

89 

55 

7 

86 

67 

58 

58 

71 

97 

39 

98 

78 

83 

16 

84 

96 

64 

8 

89 

70 

61 

62 

75 

7001 

43 

7503 

83 

88 

22 

91 

9203 

72 

91 92 

73 

64 

65 

79 

05 

47 

07 

88 

93 

27 

97 

11 

SI 

10 

5)95 

6177 

6367 

6569 

6782 

7009 

7252 

7512 

7793 

8099 

8433 

8804 

9218 

9689 

11 

98 

80 

71 

72 

86 

13 

56 

16 

98 

SI 04 

39 

10 

25 

97 

12 

6001 

83 

74 

76 

90 

17 

60 

21 

7S03 

09 

45 

17 

33 

9706 

13 

04 

86 

77 

79 

93 

21 

64 

25 

08 

15 

51 

23 

40 

14 

14 

07 

89 

80 

83 

97 

25 

68 

30 

13 

20 

57 

30 

48 

23 

15 

10 

92 

84 

86 

6801 

29 

73 

35 

17 

25 

63 

36 

55 

31 

16 

13 

95 

87 

90 

04 

33 

77 

39 

22 

31 

69 

43 

62 

40 

17 

16 

98 

90 

93 

08 

37 

81 

44 

27 

36 

74 

49 

70 

48 

18 

19 

6201 

94 

96 

12 

41 

85 

48 

32 

41 

80 

56 

77 

57 

19 

90 

05 

97 

6800 

15 

45 

89 

53 

37 

47 

86 

63 

§5 

65 

20 

6025 

6208 

6400 

6603 

6819 

7049 

7294 

7557 

7842 

8152 

8492 

8869 

9292 

9774 

21 

28 

11 

03 

07 

23 

52 

9S 

62 

47 

58 

98 

76 

9300 

83 

O.7 

31 

14 

07 

10 

26 

56 

7302 

66 

52 

63 

8504 

83 

07 

91 

23 

34 

17 

10 

14 

30 

60 

06 

71 

57 

GS 

10 

89 

15 

9800 

24 

37 

20 

13 

17 

34 

G4 

11 

76 

62 

74 

16 

96 

22 

09 

25 

40 

23 

17 

21 

38 

68 

15 

80 

67 

79 

22 

8903 

30 

17 

26 

43 

26 

20 

24 

41 

72 

19 

85 

72 

85 

28 

09 

38 

26 

27 

46 

30 

23 

28 

45 

76 

23 

89 

77 

90 

34 

16 

45 

35 

28 

49 

33 

27 

31 

49 

80 

28 

94 

82 

96 

40 

23 

53 

44 

29 

52 

36 

30 

35 

53 

84 

32 

98 

87 

8201 

46 

30 

60 

52 

30 

6055 

6239 

6433 

6639 

6856 

70S8 

7336 

7603 

7892 

8207 

8552 

8936 

9368 

9861 

31 

58 

42 

37 

42 

60 

92 

40 

08 

97 

12 

58 

43 

76 

70 

32 

61 

45 

40 

46 

64 

96 

45 

12 

7902 

18 

64 

50 

83 

79 

33 

64 

49 

43 

49 

68 

7100 

49 

17 

07 

23 

71 

57 

91 

88 

34 

67 

52 

47 

53 

71 

04 

53 

22 

12 

29 

77 

63 

99 

97 

35 

70 

55 

50 

56 

75 

IN 

58 

26 

17 

34 

83 

70 

9407 

9906 

36 

73 

58 

53 

60 

79 

12 

62 

31 

22 

40 

89 

77 

14 

15 

37 

76 

61 

57 

63 

83 

16 

66 

36 

27 

45 

95 

84 

22 

24 

38 

79 

64 

60 

67 

86 

20 

71 

40 

32 

51 

8601 

91 

30 

33 

39 

82 

68 

63 

70 

90 

24 

75 

45 

37 

56 

07 

9S 

38 

42 

40 

6085 

6271 

6467 

6674 

6894 

7128 

7379 

7650 

7942 

8262 

8614 

9005 

9445 

9951 

41 

88 

74 

70 

77 

98 

32 

84 

54 

48 

67 

20 

12 

53 

60 

42 

91 

77 

73 

81 

6901 

36 

88 

59 

53 

73 

26 

18 

61 

69 

43 

94 

80 

77 

85 

05 

40 

92 

64 

58 

79 

32 

25 

69 

78 

44 

97 

83 

80 

88 

,09 

45 

97 

68 

63 

84 

38 

32 

77 

87 

45 

6100 

87 

83 

92 

13 

49 

7401 

73 

68 

90 

44 

39 

85 

9996 

46 

04 

90 

87 

95 

17 

53 

06 

78 

73 

95 

51 

46 

93 

10005 

47 

06 

93 

90 

99 

20 

57 

10 

83 

78 

8301 

57 

53 

9501 

10015 

48 

09 

96 

94 

6702 

24 

61 

14 

87 

83 

07 

63 

60 

09 

10024 

49 

12 

99 

97 

06 

28 

65 

19 

92 

89 

12 

69 

67 

17 

10033 

60 

6115 

6303 

6500 

6710 

6932 

7169 

7423 

7697 

7994 

8318 

8676 

9074 

9525 

10043 

51 

18 

06 

04 

13 

36 

73 

27 

7702 

99 

24 

82 

81 

33 

10052 

52 

21 

09 

07 

17 

40 

77 

32 

06 

8004 

29 

88 

88 

41 

10081 

53 

24 

12 

11 

20 

43 

81 

36 

11 

091 35 

93 

96 

49 

10071 

64 

27 

15 

14 

24 

47 

85 

41 

16 

14! 41|8701 

9103 

57 

10080 

55 

30 

19 

17 

28 

51 

89 

45 

21 

20 

47 

07 

10 

65 

10089 

66 

33 

22 

21 

31 

55 

94 

49 

25 

25 

52 

14 

17 

73 

10099 

67 

36 

25 

24 

35 

59 

98 

54 

30 

30 

58 

20 

24 

81 

10108 

58 

40 

28 

28 

38 

63 

7202 

58 

35 

35 

64 

26 

31 

89 

10118 

59 

43 

32 

! 31 

| 42 

1 66 

06 

63 

40 

40 

69 

33 

38l 98 

10127 






















































Plate i 



TOw*ii?iflDn 


iff ffiwffll 




ii;mi in 

TTTTTIUi 




M 



Jp 

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e 

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u/.irt Ml > Mr? 


F'r,jiJi>v>f»ir ■ .VS 























































































































































































IK.?- S. Jones.Hotooro Xovtav 




^Ekfe4 


t lark dsl 


fYuttii •fr»// x-jrr I 


i 




































































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— 

— '— / / 


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Plate ft 








MniUtry d 1 i d 

Mr titter g Fork .. + +• + + -f •+■ 

Batten/ for Gannon .. oeT pJi./iSLtM ^ 

Battery for Mortars CC M'- -. C ^- 

Dnirtcrg . 4^ • 

Grocery " ~ I 

Court //ruse p£l 

Cotton Factory SjJ 

Tavern ...... _P-—L 

Burn tor 0= 

Glafo Factory •■’l4 

Church. c/'a Village © 

Do. Detached 4 

Foundry O E^Sl 

forge i‘/ 

(rivalry . ..... . 

Tnfa/hry fiSBEsaai-l 

House CZ3 

Mill Grist y 

C fO 

'v X '<gF 

Do. Saw vf 

Do. Strain 

Do. cC Stone * 

Do. oC Wood. cY 

/ \ 

/*wf Office- 62$l 

Trigonometrical Faint A 

7c leg rail/: L G]S i 


Tobacco P. 

Xa<£ A £ 

A 4 A UAA 
AAA i AAA 
A A A A A A A 
AAAAA % .5L 
A A A A A A A 
AAAA 4 A A 


Hire Plain V 


Gardens 


Co Hon P. 


Sugar P. 


Ploughed L. 


Orchards 


Vine yard 


Pine 


\ 4 

% 

% 

<4 

W~~ .^ 

DETAILS Of LEAVES 


■■WVj.W. 


Chesnut 


i/d ■ 


Oak 




C/-, Fy j Fruit 

imtw^ 

MHOi \- 


Pme Woods 


Heath 


i - v, ► 

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Woods 


Fresh Marsh 


Salt Marsh 


Meadows 


- a .>.-.y - • 


■« t*.-v //>A v. > 




Turnpike road 

Foot oaili 


/yy\ 

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mtmamm 


vAA/V'X Wooden Frnee.A/VVVV 
Conunmi ro«A 


mAv-% / \/V'V\A./V\A/Nv/\.A/\/\ ' 





















































































— L'lfjlcJi 


Andiorftsfe 


Ahchoxe, 


fbr f o aster 


Rocktf a’ w ays 


Harbours 


Li;<ht 


SiuvtlsomeliuiPs bare 


Chaimrl 


Fi.sb-wirs 


Lijueluue: 


slYor** -waii, ItilWrkia 






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y y 

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pspwii 


Sliore 


^<nhulm«;s 


airci 























































































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ItV 


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congress 
















































































